Runge-Kutta Methods For Rough Differential Equations, 2022 Martin Luther University Halle-Wittenberg, Institute of Mathematics, Theodor-Lieser-Str. 5, 06120 Halle (Saale), Germany

#### Runge-Kutta Methods For Rough Differential Equations, Martin Redmann, Sebastian Riedel

*Journal of Stochastic Analysis*

No abstract provided.

A Jump-Diffusion Process For Asset Price With Non-Independent Jumps, 2022 Hofstra University, Hempstead, NY 11549 USA

#### A Jump-Diffusion Process For Asset Price With Non-Independent Jumps, Yihren Wu, Majnu John

*Journal of Stochastic Analysis*

No abstract provided.

Quantization Of The Monotone Poisson Central Limit Theorem, 2022 Università di Bari, n.4, Via E. Orabona, 70125 Bari, Italy

#### Quantization Of The Monotone Poisson Central Limit Theorem, Yungang Lu

*Journal of Stochastic Analysis*

No abstract provided.

Applications Of A Superposed Ornstein-Uhlenbeck Type Processes, 2022 African Institute for Mathematical Sciences (AIMS), Cameroon

#### Applications Of A Superposed Ornstein-Uhlenbeck Type Processes, Santatriniaina Avotra Randrianambinina, Julius Esunge

*Journal of Stochastic Analysis*

No abstract provided.

On The Diagonalizability And Factorizability Of Quadratic Boson Fields, 2022 Universitá di Roma Tor Vergata, Via di Torvergata, Roma, Italy

#### On The Diagonalizability And Factorizability Of Quadratic Boson Fields, Luigi Accardi, Andreas Boukas, Yungang Lu, Alexander Teretenkov

*Journal of Stochastic Analysis*

No abstract provided.

(R1885) Analytical And Numerical Solutions Of A Fractional-Order Mathematical Model Of Tumor Growth For Variable Killing Rate, 2022 Pandit Deendayal Energy University

#### (R1885) Analytical And Numerical Solutions Of A Fractional-Order Mathematical Model Of Tumor Growth For Variable Killing Rate, N. Singha, C. Nahak

*Applications and Applied Mathematics: An International Journal (AAM)*

This work intends to analyze the dynamics of the most aggressive form of brain tumor, glioblastomas, by following a fractional calculus approach. In describing memory preserving models, the non-local fractional derivatives not only deliver enhanced results but also acknowledge new avenues to be further explored. We suggest a mathematical model of fractional-order Burgess equation for new research perspectives of gliomas, which shall be interesting for biomedical and mathematical researchers. We replace the classical derivative with a non-integer derivative and attempt to retrieve the classical solution as a particular case. The prime motive is to acquire both analytical and numerical solutions …

The Degree Gini Index Of Several Classes Of Random Trees And Their Poissonized Counterparts—Evidence For Duality, 2022 The George Washington University, Washington, DC 20052, USA

#### The Degree Gini Index Of Several Classes Of Random Trees And Their Poissonized Counterparts—Evidence For Duality, Carly Domicolo, Panpan Zhang, Hosam Mahmoud

*Journal of Stochastic Analysis*

No abstract provided.

A Sharp Rate Of Convergence In The Functional Central Limit Theorem With Gaussian Input, 2022 University of Southern California, Los Angeles, CA 90089, USA

#### A Sharp Rate Of Convergence In The Functional Central Limit Theorem With Gaussian Input, S.V. Lototsky

*Journal of Stochastic Analysis*

No abstract provided.

Quantization Of The Free Poisson Central Limit Theorem, 2022 Università di Bari, n.4, Via E. Orabona, 70125 Bari, Italy

#### Quantization Of The Free Poisson Central Limit Theorem, Yungang Lu

*Journal of Stochastic Analysis*

No abstract provided.

Quantization Of The Boolean Poisson Central Limit Theorem And A Generalized Boolean Bernoulli Sequence, 2022 Università di Bari, n.4, Via E. Orabona, 70125 Bari, Italy

#### Quantization Of The Boolean Poisson Central Limit Theorem And A Generalized Boolean Bernoulli Sequence, Yungang Lu

*Journal of Stochastic Analysis*

No abstract provided.

A First-Passage Problem For Exponential Integrated Diffusion Processes, 2022 Polytechnique Montréal, Montréal, Québec H3C 3A7, Canada

#### A First-Passage Problem For Exponential Integrated Diffusion Processes, Mario Lefebvre

*Journal of Stochastic Analysis*

No abstract provided.

Introduction To Mathematical Analysis I - 3rd Edition, 2022 Portland State University

#### Introduction To Mathematical Analysis I - 3rd Edition, Beatriz Lafferriere, Gerardo Lafferriere, Mau Nam Nguyen

*PDXOpen: Open Educational Resources*

Video lectures explaining problem solving strategies are available

Our goal in this set of lecture notes is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs.

The lecture notes contain topics of real analysis usually covered in a 10-week course: the completeness axiom, sequences and convergence, continuity, and differentiation. In addition, the notes include many carefully selected exercises of various levels …

Proving Dirichlet's Theorem On Arithmetic Progressions, 2022 Western University

#### Proving Dirichlet's Theorem On Arithmetic Progressions, Owen T. Abma

*Undergraduate Student Research Internships Conference*

First proved by German mathematician Dirichlet in 1837, this important theorem states that for coprime integers a, m, there are an infinite number of primes p such that p = a (mod m). This is one of many extensions of Euclid’s theorem that there are infinitely many prime numbers. In this paper, we will formulate a rather elegant proof of Dirichlet’s theorem using ideas from complex analysis and group theory.

Domain Of Exotic Laplacian Constructed By Wiener Integrals Of Exponential White Noise Distributions, 2022 Universitá di Roma Tor Vergata, Via di Torvergata, Roma, Italy

#### Domain Of Exotic Laplacian Constructed By Wiener Integrals Of Exponential White Noise Distributions, Luigi Accardi, Un Cig Ji, Kimiaki Saitô

*Journal of Stochastic Analysis*

No abstract provided.

On The Thom Isomorphism For Groupoid-Equivariant Representable K-Theory, 2022 Dartmouth College

#### On The Thom Isomorphism For Groupoid-Equivariant Representable K-Theory, Zachary J. Garvey

*Dartmouth College Ph.D Dissertations*

This thesis proves a general Thom Isomorphism in groupoid-equivariant KK-theory. Through formalizing a certain pushforward functor, we contextualize the Thom isomorphism to groupoid-equivariant representable K-theory with various support conditions. Additionally, we explicitly verify that a Thom class, determined by pullback of the Bott element via a generalized groupoid homomorphism, coincides with a Thom class defined via equivariant spinor bundles and Clifford multiplication. The tools developed in this thesis are then used to generalize a particularly interesting equivalence of two Thom isomorphisms on TX, for a Riemannian G-manifold X.

The Art Of Analysis, 2022 Connecticut College

#### The Art Of Analysis, Christopher Hammond

*Open Educational Resources*

Christopher Hammond, Professor of Mathematics at Connecticut College, has written an introductory textbook in real analysis. This resource is freely available for anyone to use, either individually or in a classroom setting.

The primary innovation of this text is a new perspective on teaching the theory of integration. Most introductory analysis courses focus initially on the Riemann integral, with other definitions discussed later (if at all). The paradigm being proposed is that the Riemann integral and the “generalized Riemann integral” should be considered simultaneously, not separately – in the same manner as uniform continuity and continuity. Riemann integrability is simply …

Improving Computation For Hierarchical Bayesian Spatial Gaussian Mixture Models With Application To The Analysis Of Thz Image Of Breast Tumor, 2022 University of Arkansas, Fayetteville

#### Improving Computation For Hierarchical Bayesian Spatial Gaussian Mixture Models With Application To The Analysis Of Thz Image Of Breast Tumor, Jean Remy Habimana

*Graduate Theses and Dissertations*

In the first chapter of this dissertation we give a brief introduction to Markov chain Monte Carlo methods (MCMC) and their application in Bayesian inference. In particular, we discuss the Metropolis-Hastings and conjugate Gibbs algorithms and explore the computational underpinnings of these methods. The second chapter discusses how to incorporate spatial autocorrelation in linear a regression model with an emphasis on the computational framework for estimating the spatial correlation patterns.

The third chapter starts with an overview of Gaussian mixture models (GMMs). However, because in the GMM framework the observations are assumed to be independent, GMMs are less effective when …

Perturbation - For Nature Computes On A Straight Line (In Seven Balancing Acts), 2022 Claremont Colleges

#### Perturbation - For Nature Computes On A Straight Line (In Seven Balancing Acts), Vijay Fafat

*Journal of Humanistic Mathematics*

What if all of our Reality is a simulation? What, perhaps, are the unintended artifacts if we are an "approximate" simulation because God could not muster sufficient computational power for the Equations capturing the ultimate Theory of Everything? Are life and Sentience something She intended, a problem with the simulation's code, or an irreducible, teleological inevitability in Creation?

The Construction And Estimation Of Hidden Semi-Markov Models, 2022 University of Sulaimani, Sulaymaniyah, Iraq

#### The Construction And Estimation Of Hidden Semi-Markov Models, Kurdstan Abdullah, John Van Der Hoek

*Journal of Stochastic Analysis*

No abstract provided.

Random Walks In The Quarter Plane: Solvable Models With An Analytical Approach, 2022 DePaul University

#### Random Walks In The Quarter Plane: Solvable Models With An Analytical Approach, Harshita Bali, Enrico Au-Yeung

*DePaul Discoveries*

Initially, an urn contains 3 blue balls and 1 red ball. A ball is randomly chosen from the urn. The ball is returned to the urn, together with one additional ball of the same type (red or blue). When the urn has twenty balls in it, what is the probability that exactly ten balls are blue? This is a model for a random process. This urn model has been extended in various ways and we consider some of these generalizations. Urn models can be formulated as random walks in the quarter plane. Our findings indicate that for a specific type …