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Articles 1 - 30 of 34
Full-Text Articles in Other Statistics and Probability
Impact Of Urban Development On Uv Exposure: A Clustering And Machine Learning Assessment, Taufik Roni Sahroni Mr., Verdi Yasin, Lulut Alfaris, Reza Ariefka, Ruben Cornelius Siagian, Mohammad Alfin Karim, Nana Rahdiana, Ade Suhara
Impact Of Urban Development On Uv Exposure: A Clustering And Machine Learning Assessment, Taufik Roni Sahroni Mr., Verdi Yasin, Lulut Alfaris, Reza Ariefka, Ruben Cornelius Siagian, Mohammad Alfin Karim, Nana Rahdiana, Ade Suhara
Journal of Environmental Science and Sustainable Development
The relocation of Indonesia's capital city is anticipated to promote inclusive economic growth while embracing cultural diversity. However, this transition may affect ultraviolet (UV) radiation exposure patterns. The study investigated variations in UV exposure in the IKN region, focusing on urban development factors such as land use and population density that affect public health, sun protection, and skin cancer prevention. The research hypothesized that UV radiation is significantly correlated with these factors. UV Index data from 2010-2023, a hierarchical clustering method, identifies complex data patterns without determining the number of clusters. XGBoost, a machine learning model, was used for handling …
(R2101) Analysis Of Map/Ph/1 Queueing Inventory System With Two Commodity, Working Vacation, (S, S) Replenishment Policy, Essential And Optional Repair, G. Ayyappan, N. Arulmozhi
(R2101) Analysis Of Map/Ph/1 Queueing Inventory System With Two Commodity, Working Vacation, (S, S) Replenishment Policy, Essential And Optional Repair, G. Ayyappan, N. Arulmozhi
Applications and Applied Mathematics: An International Journal (AAM)
We examine a queueing inventory model with single server which can offer two types of inventory items: main item (commodity I) and complementary item (commodity II). We assume both commodities have a finite capacity Si, i = 1, 2. Customers reach the system by following the Markovian arrival process (MAP). The service times are considered to be phase-type (PH) distribution. We have considered no customer in the system, even inventory level is positive; the server will start the working vacation, and any customer that arrives during working vacation, the server provides slow service. If an item is not available, the …
Striking A Balance: Market Shock & Responses In Automotive Components Manufacturing, Emma Lane Mcgahey
Striking A Balance: Market Shock & Responses In Automotive Components Manufacturing, Emma Lane Mcgahey
All Theses
This thesis examines the effects of extreme market shocks on supply chain dynamics within the automotive industry. Through an analysis of demand data from an automotive manufacturer to its component suppliers (January 2018 to May 2024), the study investigates the relationship between market shocks and supply chain responses, providing insights into how auto components inventory management handles downstream responses to market shocks. With supporting public data—from FRED, BLS, and the U.S. Census Bureau resources—we explore two primary relationships: the impact of market shocks on the Average Standard Deviation of Demand (SDO) and the effect of demand variability on expedited pricing …
Decoding Neural Networks: An Information-Theoretic Guide To Interpretability, Error Analysis And Efficiency, Mackenzie J. Meni
Decoding Neural Networks: An Information-Theoretic Guide To Interpretability, Error Analysis And Efficiency, Mackenzie J. Meni
Theses and Dissertations
This dissertation addresses critical challenges in neural network design by leveraging entropy-based techniques to improve model efficiency, interpretability, and bias reduction. Focusing on the unique demands of computer vision applications, particularly object detection and classification for real-time systems, this work introduces a series of innovative methods centered on information theory. At the core of these methods is the Probabilistic Explanations of Entropic Knowledge (PEEK) framework, a tool developed to analyze and visualize entropy distributions across feature maps. PEEK offers insights into information flow within neural networks, making it possible to pinpoint layers that contribute meaningfully to decision-making or identify those …
Evaluating Trauma-Informed Design In A Mental Health Setting: A Community-Based Research Case Study, Marie Spence
Evaluating Trauma-Informed Design In A Mental Health Setting: A Community-Based Research Case Study, Marie Spence
Electronic Theses and Dissertations
This case study utilized a community-based research framework to explore how the Trauma-Informed Design framework can be implemented in a mental health setting. This study focused on the site of Empower Therapy Practice, a private mental health practice in the Denver Metro Area, to engage clients and staff to participate in advisory boards and inform the interior design of a new office space. To explore the application of Trauma-Informed Design, participants engaged in a variety of research activities, including an evaluative questionnaire, Photovoice, and focus group. Advisory board members identified various aspects of Trauma-Informed Design which meaningfully translate to therapeutic …
Human Capital At Home: Evidence From A Randomized Evaluation In The Philippines, Noam Angrist, Sarah Kabay, Dean S. Karlan, Lincoln Lau, Kevin M. Wong
Human Capital At Home: Evidence From A Randomized Evaluation In The Philippines, Noam Angrist, Sarah Kabay, Dean S. Karlan, Lincoln Lau, Kevin M. Wong
Education Division Scholarship
Children spend most of their time at home in their early years, yet efforts to promote human capital at home in many low- and middle-income settings remain limited. We conduct a randomized controlled trial to evaluate an intervention which encourages parents and caregivers to foster human capital accumulation among their children between ages 3 and 5, with a focus on math and phonics skills. Children gain 0.52 and 0.51 standard deviations relative to the control group on math and phonics tests, respectively (p<0.001). A year later effects persist, but math gains dissipate to 0.15 (p=0.06) and phonics to 0.13 (p=0.12). Effects appear to be mediated largely through instructional support by parents and not other parent investment mechanisms, such as more positive parent-child interactions or additional time spent on education at home beyond the intervention. Our results show that parents can be effective conduits of educational instruction even in low-resource settings.
The Naked Truth Of My Voice: Surveying The Soul Of An Aspiring Educator From Dusk To Dawn: An Arts-Based Auto-Criticism Inquiry, Siddharth Maan
The Naked Truth Of My Voice: Surveying The Soul Of An Aspiring Educator From Dusk To Dawn: An Arts-Based Auto-Criticism Inquiry, Siddharth Maan
Electronic Theses and Dissertations
This dissertation is based on auto-criticism, a new qualitative inquiry that combines educational criticism and arts-based research. It focuses on my own experiences as an aspiring educator who struggles with stuttering and public speaking anxiety. The study aims to describe, interpret, evaluate, and thematize my experiences of dealing with public speaking anxiety and stuttering before, during, and after classroom teaching. In addition, this dissertation highlights the potential contributions of auto-criticism as a methodology to qualitative research and higher education. I utilized journaling to document data. Photos and music were also used to enhance the understanding of my lived experiences and …
A Uniformly Most Powerful Test For The Mean Of A Beta Distribution, Richard Ntiamoah Kyei
A Uniformly Most Powerful Test For The Mean Of A Beta Distribution, Richard Ntiamoah Kyei
Electronic Theses and Dissertations
The beta distribution is used in numerous real-world applications, including areas such as manufacturing (quality control) and analyzing patient outcomes in health care. It also plays a key role in statistical theory, including multivariate analysis of variance (MANOVA) and Bayesian statistics. It is a flexible distribution that can account for many different characteristics of real data. To our surprise, there has been very little work or discussion on performing statistical hypothesis testing for the mean when it is reasonable to assume that the population is beta distributed. Many analysts conduct traditional analyses using a t-test or nonparametric approach, try transformations, …
Exploring Healthcare Chatbot Information Presentation: Applying Hierarchical Bayesian Regression And Inductive Thematic Analysis In A Mixed Methods Study, Samuel Nelson Koscelny
Exploring Healthcare Chatbot Information Presentation: Applying Hierarchical Bayesian Regression And Inductive Thematic Analysis In A Mixed Methods Study, Samuel Nelson Koscelny
All Theses
High blood pressure, also known as hypertension, significantly increases the risk of heart disease and stroke, which are leading causes of death in the United States. While contributing to over 691,000 deaths in 2021 alone in the United States (U.S.), it also imposes immense economic burden on the healthcare system, costing approximately $131 billion annually. One way to address this issue is for increased self-care behaviors and medication adherence, both of which require sufficient health literacy. Despite the importance of health literacy, 90% of U.S. adults struggle with health-related subjects. Overcoming the issues associated with health literacy requires addressing the …
Emotionality Stigma Scale: Measurement Development, Reliability, And Validity., Hayley D. Seely
Emotionality Stigma Scale: Measurement Development, Reliability, And Validity., Hayley D. Seely
Electronic Theses and Dissertations
Emotions are biological responses to stimuli that allow individuals to derive meaning, appraise experiences, and prepare to respond. However, individuals perceive emotions differently based on emotion socialization which not only dictates the way emotions are viewed and managed but also has been directly linked with mental health outcomes. Furthermore, research shows emotion socialization is informed by demographic variables such as gender such that the expectations of emotionality differ; where women are taught to express emotions, men are taught to conceal. Given the societal rules regarding emotionality, it is possible that emotionality stigma – the stigma around the experience and expression …
Comparing The Preparation Of Youth Services Librarians To Their On-The-Ground Experiences: A Grounded Theory Study Incorporating Criticism And Connoisseurship, Anne Holland
Electronic Theses and Dissertations
The purpose of this study was to better understand the on-the-ground preparation of youth services librarians, in contrast to their professional training in Master’s of Library Science (MLIS) programs. Classic Grounded Theory was the predominant methodology for this qualitative study, and elements of Criticism and Connoisseurship were also utilized. Document review, interviews, and journaling activities with ten participants were the primary methods of data collection. Key findings from this dissertation include a grounded theory explaining the current state of preparation for youth services librarianship, and multiple avenues for further study.
Extending The Utility Of Ant Colony Optimization Through The Incorporation Of An Intraclass Correlation Coefficient To Assess For Rater Consistency, Mark Leveling
Electronic Theses and Dissertations
Ant Colony Optimization (ACO) is a flexible algorithm designed to solve complex combinatorial problems. While the method was derived from the behavior of ants by researchers in the field of computer science, its application to solving complex combinatorial problems is widespread in a growing number of fields in behavioral science, including psychometrics. Over the last two decades, psychometricians have adapted ACO to measurement model specification problems with the intention of generating measurement models that express measurement model fit and reliability within the standards of what is considered acceptable. Additionally, psychometricians have used ACO to generate shortened versions of existing measures …
Topological Regression As An Interpretable And Efficient Tool For Quantitative Structureactivity Relationship Modeling, Ruibo Zhang, Daniel Nolte, Cesar Sanchez-Villalobos, Souparno Ghosh, Ranadip Pal
Topological Regression As An Interpretable And Efficient Tool For Quantitative Structureactivity Relationship Modeling, Ruibo Zhang, Daniel Nolte, Cesar Sanchez-Villalobos, Souparno Ghosh, Ranadip Pal
Department of Statistics: Faculty Publications
Quantitative structure-activity relationship (QSAR)modeling is a powerful tool for drug discovery, yet the lack of interpretability of commonly used QSAR models hinders their application inmolecular design.We propose a similaritybased regression framework, topological regression (TR), that offers a statistically grounded, computationally fast, and interpretable technique to predict drug responses. We compare the predictive performance of TR on 530 ChEMBL human target activity datasets against the predictive performance of deep-learning-based QSAR models. Our results suggest that our sparse TR model can achieve equal, if not better, performance than the deep learningbased QSAR models and provide better intuitive interpretation by extracting an approximate …
Value Added Tax Rate Variation, Import Demand And Sectoral Output In Nigeria, Joshua K. Nomkuha, Aondoawase Asooso, Philip T. Abachi
Value Added Tax Rate Variation, Import Demand And Sectoral Output In Nigeria, Joshua K. Nomkuha, Aondoawase Asooso, Philip T. Abachi
CBN Journal of Applied Statistics (JAS)
This study employs computable general equilibrium (CGE) model to estimate the effect of increase in value added tax (VAT), from 5 per cent to 7.5 per cent, on import demand and sectoral output in Nigeria. The study uses 2020 as the base year for the data analysis. The results show that increase in VAT affects import demand negatively, based on import penetration ratios, with mixed effect across six sectors. The implication of the result is that the VAT policy discourage consumption of foreign products, and constitute excess burden to consumers of such products in Nigeria. The results further reveal that …
Stock Market Volatility In The United Kingdom: Simulating Post-Covid-19 Recovery, Bala A. Dahiru, Mohammed Shuaibu, Najibullah Hassanov
Stock Market Volatility In The United Kingdom: Simulating Post-Covid-19 Recovery, Bala A. Dahiru, Mohammed Shuaibu, Najibullah Hassanov
CBN Journal of Applied Statistics (JAS)
This paper investigates the time it would take for the FTSE-100 index to reach its post-COVID-19 peak. The paper utilises an exponential generalised autoregressive conditional heteroscedasticity (EGARCH) model that accounts for leverage effect and asymmetries. The preferred models amongst competing variants was the Autoregressive Moving Average (ARMA)-EGARCH(2,1) specification and was used to predict daily FTSE-100 data from 5th January 2000 to 21st June 2024. The empirical exercise showed that the COVID-19-induced financial crisis negatively affected the United Kingdom’s stock market performance. The results show that the FTSE100 index could reach its post-pandemic peak around 27th August, 2024 (two months after …
Recursive Marix Game Analysis: Optimal, Simplified, And Human Strategies In Brave Rats, William A. Medwid
Recursive Marix Game Analysis: Optimal, Simplified, And Human Strategies In Brave Rats, William A. Medwid
Master's Theses
Brave Rats is a short game with simple rules, yet establishing a comprehensive strategy is very challenging without extensive computation. After explaining the rules, this paper begins by calculating the optimal strategy by recursively solving each turn’s Minimax strategy. It then provides summary statistics about the complex, branching Minimax solution. Next, we examine six other strategy models and evaluate their performance against each other. These models’ flaws highlight the key elements that contribute to the effectiveness of the Minimax strategy and offer insight into simpler strategies that human players could mimic. Finally, we analyze 123 games of human data collected …
Bagging Improves The Performance Of Deep Learning-Based Semantic Segmentation With Limited Labeled Images: A Case Study Of Crop Segmentation For High-Throughput Plant Phenotyping, Yinglun Zhan, Yuzhen Zhou, Geng Bai, Yufeng Ge
Bagging Improves The Performance Of Deep Learning-Based Semantic Segmentation With Limited Labeled Images: A Case Study Of Crop Segmentation For High-Throughput Plant Phenotyping, Yinglun Zhan, Yuzhen Zhou, Geng Bai, Yufeng Ge
Department of Statistics: Faculty Publications
Advancements in imaging, computer vision, and automation have revolutionized various fields, including field-based high-throughput plant phenotyping (FHTPP). This integration allows for the rapid and accurate measurement of plant traits. Deep Convolutional Neural Networks (DCNNs) have emerged as a powerful tool in FHTPP, particularly in crop segmentation—identifying crops from the background—crucial for trait analysis. However, the effectiveness of DCNNs often hinges on the availability of large, labeled datasets, which poses a challenge due to the high cost of labeling. In this study, a deep learning with bagging approach is introduced to enhance crop segmentation using high-resolution RGB images, tested on the …
Towards A New Role Of Mitochondrial Hydrogen Peroxide In Synaptic Function, Cliyahnelle Z. Alexander
Towards A New Role Of Mitochondrial Hydrogen Peroxide In Synaptic Function, Cliyahnelle Z. Alexander
Student Theses and Dissertations
Aerobic metabolism is known to generate damaging ROS, particularly hydrogen peroxide. Reactive oxygen species (ROS) are highly reactive molecules containing oxygen that have the potential to cause damage to cells and tissues in the body. ROS are highly reactive atoms or molecules that rapidly interact with other molecules within a cell. Intracellular accumulation can result in oxidative damage, dysfunction, and cell death. Due to the limitations of H2O2 (hydrogen peroxide) detectors, other impacts of ROS exposure may have been missed. HyPer7, a genetically encoded sensor, measures hydrogen peroxide emissions precisely and sensitively, even at sublethal levels, during …
The Quantitative Analysis And Visualization Of Nfl Passing Routes, Sandeep Chitturi
The Quantitative Analysis And Visualization Of Nfl Passing Routes, Sandeep Chitturi
Computer Science and Computer Engineering Undergraduate Honors Theses
The strategic planning of offensive passing plays in the NFL incorporates numerous variables, including defensive coverages, player positioning, historical data, etc. This project develops an application using an analytical framework and an interactive model to simulate and visualize an NFL offense's passing strategy under varying conditions. Using R-programming and data management, the model dynamically represents potential passing routes in response to different defensive schemes. The system architecture integrates data from historical NFL league years to generate quantified route scores through designed mathematical equations. This allows for the prediction of potential passing routes for offensive skill players in response to the …
Selected Topics On Sequential Designs For Decision Making, Caroline Kerfonta
Selected Topics On Sequential Designs For Decision Making, Caroline Kerfonta
All Dissertations
This dissertation is comprised of three parts. The first proposes a sequential approach to determine the experimental setting with the minimum variance (Kerfonta et al., 2024). Two acquisition functions are developed to assist developing the approach. Theoretical results along with a case study using data from crystallization experiments is conducted to show the ability of the proposed method to correctly select the experiment with the minimum variance. The second and third parts propose adaptations to the Bayesian optimization algorithm using transformed additive Gaussian processes (TAG) as the surrogate model. The goal of using the TAG framework is to decompose the …
Artificial Intelligence Could Probably Write This Essay Better Than Me, Claire Martino
Artificial Intelligence Could Probably Write This Essay Better Than Me, Claire Martino
Augustana Center for the Study of Ethics Essay Contest
No abstract provided.
Phenomenological Inquiry Into Middle School Teachers’ Perception Of Creativity, Katalin Grajzel
Phenomenological Inquiry Into Middle School Teachers’ Perception Of Creativity, Katalin Grajzel
Electronic Theses and Dissertations
Researchers do agree that creativity is an ability that can be developed and should be fostered (Guilford, 1958; Parnes, 1961). Teachers play an important role in creativity development and often serve as gatekeepers to identify gifted and talented students (Bianco et al., 2011; Novak & Jones, 2021; Schack & Starko, 1990). However, teachers’ judgment of their students’ creativity often only correlates weakly with the results of creativity measures (Kettler et al., 2018; Torrance, 1963). Therefore, in this study I explored teachers’ perception of creativity and creative students as well as factors that support or hinder creativity. The findings revealed that …
Editorial: Ipps 2022 - Plant Phenotyping For A Sustainable Future, Elias Kaiser, Philipp Von Gillhaussen, Jennifer Clarke, Ulrich Schurr
Editorial: Ipps 2022 - Plant Phenotyping For A Sustainable Future, Elias Kaiser, Philipp Von Gillhaussen, Jennifer Clarke, Ulrich Schurr
Department of Statistics: Faculty Publications
Plants are a venue for addressing the challenges facing humanity. The need for a reliable supply of food, feed, materials, chemicals and energy as well as ways to manage agroecology and climate change are among the challenges that we can address through the sustainable use of plants and plant ecosystems. The research community needs to integrate plant systems approaches, from molecular to organismal to applications in the field and ecosystems, to increase productivity sustainably while using fewer land, water, and nutrient resources. In the past two decades, plant phenotyping research has developed a highly valuable portfolio of technologies, processes and …
Discussion On “Spatial+: A Novel Approach To Spatial Confounding” By Dupont, Wood, And Augustin, Brian J. Reich, Shu Yang, Yawen Guan
Discussion On “Spatial+: A Novel Approach To Spatial Confounding” By Dupont, Wood, And Augustin, Brian J. Reich, Shu Yang, Yawen Guan
Department of Statistics: Faculty Publications
Congratulations to the authors for this thoughtful and timely contribution to the spatial confounding literature. The intuitive nature of the method and simplicity of the estimation procedure will surely make Spatial+ popular with practitioners, and the theoretical developments are a major advance for researchers in this area. There is much to discuss! We have formatted our discussion in two sections: in Section 2 we consider the assumptions and statistical properties of Spatial+, and in Section 3 we examine how Spatial+ fits in the wider literature on spatial causal inference.
Prebiotic Proanthocyanidins Inhibit Bile Reflux–Induced Esophageal Adenocarcinoma Through Reshaping The Gut Microbiome And Esophageal Metabolome, Katherine M. Weh, Connor L. Howard, Yun Zhang, Bridget A. Tripp, Jennifer Clarke, Amy B. Howell, Joel H. Rubenstein, Julian A. Abrams, Maria Westerhoff, Laura A. Kresty
Prebiotic Proanthocyanidins Inhibit Bile Reflux–Induced Esophageal Adenocarcinoma Through Reshaping The Gut Microbiome And Esophageal Metabolome, Katherine M. Weh, Connor L. Howard, Yun Zhang, Bridget A. Tripp, Jennifer Clarke, Amy B. Howell, Joel H. Rubenstein, Julian A. Abrams, Maria Westerhoff, Laura A. Kresty
Department of Statistics: Faculty Publications
The gut and local esophageal microbiome progressively shift from healthy commensal bacteria to inflammation-linked pathogenic bacteria in patients with gastroesophageal reflux disease, Barrett’s esophagus, and esophageal adenocarcinoma (EAC). However, mechanisms by which microbial communities and metabolites contribute to reflux-driven EAC remain incompletely understood and challenging to target. Herein, we utilized a rat reflux-induced EAC model to investigate targeting the gut microbiome–esophageal metabolome axis with cranberry proanthocyanidins (C-PAC) to inhibit EAC progression. Sprague-Dawley rats, with or without reflux induction, received water or C-PAC ad libitum (700 μg/rat/day) for 25 or 40 weeks. C-PAC exerted prebiotic activity abrogating reflux-induced dysbiosis and mitigating …
Mapping Urban Form Into Local Climate Zones For The Continental Us From 1986–2020, Meng Qi, Chunxue Xu, Wenwen Zhang, Matthias Demuzere, Perry Hystad, Tianjun Lu, Peter James, Benjamin Bechtel, Steve Hankey
Mapping Urban Form Into Local Climate Zones For The Continental Us From 1986–2020, Meng Qi, Chunxue Xu, Wenwen Zhang, Matthias Demuzere, Perry Hystad, Tianjun Lu, Peter James, Benjamin Bechtel, Steve Hankey
Earth and Environmental Sciences Faculty Publications
Urbanization has altered land surface properties driving changes in micro-climates. Urban form influences people’s activities, environmental exposures, and health. Developing detailed and unified longitudinal measures of urban form is essential to quantify these relationships. Local Climate Zones [LCZ] are a culturally-neutral urban form classification scheme. To date, longitudinal LCZ maps at large scales (i.e., national, continental, or global) are not available. We developed an approach to map LCZs for the continental US from 1986 to 2020 at 100 m spatial resolution. We developed lightweight contextual random forest models using a hybrid model development pipeline that leveraged crowdsourced and expert labeling …
On The Transmuted Distributions; Properties And Application, Jacob D. Kretzer
On The Transmuted Distributions; Properties And Application, Jacob D. Kretzer
Theses, Dissertations and Capstones
The transmuted distributions first appeared in (2007) after Shaw and Buckley constructed a quadratic rank transmutation map (QRTM), G(u) = (1 + λ)u − λu2, as a transformation of a cumulative distribution function of a random variable X, to generate the transmuted-X distribution. In (2017), Jayakumar & Babu defined the T -transmuted-X family of distributions by incorporating a transmuted-X into a transformer-transformed class of distributions (Aljarrah et al., 2014). This thesis surveys the main properties of the transmuted-X distribution, such as density shapes, moments, and entropy. Detailed attention will be given …
Using Ai For Qualitative Labeling: Consistency And Comparisons, James Mcintyre
Using Ai For Qualitative Labeling: Consistency And Comparisons, James Mcintyre
Honors Program Theses
This paper details a research study evaluating AI's ability to perform qualitative deductive coding. Multiple AI models were utilized and compared against three human coders and one expert coder. A series of 107 statements were sourced from a group discussion for a qualitative impact assessment of an organization. The AI models were provided these statements and directed to code them using the Community Capitals Framework. Two generations of AI models were evaluated. Overall, the AI achieved a fair level of agreement with the human annotators, but the alignment was far from perfect. Newer AI models did not increase agreement with …
Examining Stigma In Rural Mental Health Care Settings: A Mixed Methods Approach, Lainie Krumenacker
Examining Stigma In Rural Mental Health Care Settings: A Mixed Methods Approach, Lainie Krumenacker
Murray State Theses and Dissertations
More than half of Americans will be diagnosed with a mental illness in their lifetime (CDC, 2021), yet stigma towards mental health affects both patients and providers. Although programs exist to address stigma, improve cultural competency among providers, and educate families on the importance of support, facilities are often limited on programs they provide due to allocation of resources and funds. Without a shift in treatment and programing, stigma will continue to impact patient care and outcome.
This study explored stigma among mental health providers in rural communities, while exploring potential differences in treatment among patients due to race. Mental …
Last Passage Time And Excursion Theory For Solvable Diffusions With Applications In Mathematical Finance, Yaode Sui
Theses and Dissertations (Comprehensive)
In this dissertation, we investigate the properties of last passage times and excursion theory in one-dimensional solvable diffusions, emphasizing their applications in financial modeling, particularly in option pricing. We derive closed-form formulas for the marginal distribution of last passage times and their joint distribution with process values, including the maximum and minimum of the process value. The focus is on time-homogeneous diffusions with various boundaries and imposed killing. Employing spectral expansion theory, we derive explicit formulas for distributions of last passage times in common processes such as Drifted Brownian Motion (BM), Squared Bessel (SQB), Ornstein-Uhlenbeck (OU), and Cox-Ingersoll-Ross (CIR) models. …