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- Knot theory (2)
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- Anticipation (1)
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Articles 1 - 30 of 38
Full-Text Articles in Entire DC Network
Runge-Kutta Methods For Rough Differential Equations, Martin Redmann, Sebastian Riedel
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, Yihren Wu, Majnu John
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, Yungang Lu
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, Santatriniaina Avotra Randrianambinina, Julius Esunge
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, Luigi Accardi, Andreas Boukas, Yungang Lu, Alexander Teretenkov
On The Diagonalizability And Factorizability Of Quadratic Boson Fields, Luigi Accardi, Andreas Boukas, Yungang Lu, Alexander Teretenkov
Journal of Stochastic Analysis
No abstract provided.
Fractal Like Snowflakes Generated By Non-Contractive Function Systems, William H. Kelly Iii
Fractal Like Snowflakes Generated By Non-Contractive Function Systems, William H. Kelly Iii
LSU Master's Theses
At the heart of this thesis is the examination of a non-contractive iterative function system T on the Hausdorff metric space of all compact subset of ℝ . Despite the absence of an 2 attracting fixed point, an examination reveals the appearance of fractal-like shapes (snowflakes) when applying the Barnsley’ random walk method to study the iterative sequence ��n(0) (�� ∈ ℕ) for �� = ��1 ∪ ��2 ∪ ��3, where ��1(��) = ����, ��2(��) = ���� + ��, and ��3(��) = ���� - ��, and �� = …
The Degree Gini Index Of Several Classes Of Random Trees And Their Poissonized Counterparts—Evidence For Duality, Carly Domicolo, Panpan Zhang, Hosam Mahmoud
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 Cluster Structure On The Coordinate Ring Of Partial Flag Varieties, Fayadh Kadhem
A Cluster Structure On The Coordinate Ring Of Partial Flag Varieties, Fayadh Kadhem
LSU Doctoral Dissertations
The main goal of this dissertation is to show that the (multi-homogeneous) coordinate ring of a partial flag variety C[G/P_K^−] contains a cluster algebra for every semisimple complex algebraic group G. We use derivation properties and a canonical lifting map to prove that the cluster algebra structure A of the coordinate ring C[N_K] of a Schubert cell constructed by Goodearl and Yakimov can be lifted, in an explicit way, to a cluster structure \hat{A} living in the coordinate ring of the corresponding partial flag variety. Then we use a minimality condition to prove that the cluster algebra \hat{A} is equal …
A Sharp Rate Of Convergence In The Functional Central Limit Theorem With Gaussian Input, S.V. Lototsky
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, Yungang Lu
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, Yungang Lu
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, Mario Lefebvre
A First-Passage Problem For Exponential Integrated Diffusion Processes, Mario Lefebvre
Journal of Stochastic Analysis
No abstract provided.
Domain Of Exotic Laplacian Constructed By Wiener Integrals Of Exponential White Noise Distributions, Luigi Accardi, Un Cig Ji, Kimiaki Saitô
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.
The Construction And Estimation Of Hidden Semi-Markov Models, Kurdstan Abdullah, John Van Der Hoek
The Construction And Estimation Of Hidden Semi-Markov Models, Kurdstan Abdullah, John Van Der Hoek
Journal of Stochastic Analysis
No abstract provided.
The Thermodynamics Of A Stochastic Geometry Model With Applications To Non-Extensive Statistics, O.K. Kazemi, A. Pourdarvish, J. Sadeghi
The Thermodynamics Of A Stochastic Geometry Model With Applications To Non-Extensive Statistics, O.K. Kazemi, A. Pourdarvish, J. Sadeghi
Journal of Stochastic Analysis
No abstract provided.
Quantization Of The Poisson Type Central Limit Theorem (1), Yungang Lu
Quantization Of The Poisson Type Central Limit Theorem (1), Yungang Lu
Journal of Stochastic Analysis
No abstract provided.
Commutative C*-Algebras Generated By Toeplitz Operators On The Fock Space, Vishwa Nirmika Dewage
Commutative C*-Algebras Generated By Toeplitz Operators On The Fock Space, Vishwa Nirmika Dewage
LSU Doctoral Dissertations
The Fock space $\mathcal{F}(\mathbb{C}^n)$ is the space of holomorphic functions on $\mathbb{C}^n$ that are square-integrable with respect to the Gaussian measure on $\mathbb{C}^n$. This space plays an essential role in several subfields of analysis and representation theory. In particular, it has for a long time been a model to study Toeplitz operators. Grudsky and Vasilevski showed in 2002 that radial Toeplitz operators on $\mathcal{F}(\mathbb{C})$ generate a commutative $C^*$-algebra $\mathcal{T}^G$, while Esmeral and Maximenko showed that $C^*$-algebra $\mathcal{T}^G$ is isometrically isomorphic to the $C^*$-algebra $C_{b,u}(\mathbb{N}_0,\rho_1)$. In this thesis, we extend the result to $k$-quasi-radial symbols acting on the Fock space $\mathcal{F}(\mathbb{C}^n)$. …
On A Relation Between Ado And Links-Gould Invariants, Nurdin Takenov
On A Relation Between Ado And Links-Gould Invariants, Nurdin Takenov
LSU Doctoral Dissertations
In this thesis we consider two knot invariants: Akutsu-Deguchi-Ohtsuki(ADO) invariant and Links-Gould invariant. They both are based on Reshetikhin-Turaev construction and as such share a lot of similarities. Moreover, they are both related to the Alexander polynomial and may be considered generalizations of it. By experimentation we found that for many knots, the third order ADO invariant is a specialization of the Links-Gould invariant. The main result of the thesis is a proof of this relation for a large class of knots, specifically closures of braids with five strands.
A Closed Form Formula For The Stochastic Exponential Of A Matrix-Valued Semimartingale, Peter Kern, Christian Müller
A Closed Form Formula For The Stochastic Exponential Of A Matrix-Valued Semimartingale, Peter Kern, Christian Müller
Journal of Stochastic Analysis
No abstract provided.
Self-Repelling Elastic Manifolds With Low Dimensional Range, Carl Mueller, Eyal Neumann
Self-Repelling Elastic Manifolds With Low Dimensional Range, Carl Mueller, Eyal Neumann
Journal of Stochastic Analysis
No abstract provided.
Induced Matrices: Recurrences And Markov Chains, Philip Feinsilver
Induced Matrices: Recurrences And Markov Chains, Philip Feinsilver
Journal of Stochastic Analysis
No abstract provided.
On Uniqueness And Stability For The Boltzmann-Enskog Equation, Martin Friesen, Barbara Ruediger, Padmanabhan Subdar
On Uniqueness And Stability For The Boltzmann-Enskog Equation, Martin Friesen, Barbara Ruediger, Padmanabhan Subdar
Faculty Publications
The time-evolution of a moderately dense gas in a vacuum is described in classical mechanics by a particle density function obtained from the Boltzmann-Enskog equation. Based on a McKean-Vlasov equation with jumps, the associated stochastic process was recently constructed by modified Picard iterations with the mean-field interactions, and more generally, by a system of interacting particles. By the introduction of a shifted distance that exactly compensates for the free transport term that accrues in the spatially inhomogeneous setting, we prove in this work an inequality on the Wasserstein distance for any two measure-valued solutions to the Boltzmann-Enskog equation. As a …
Anticipating Stochastic Integrals And Related Linear Stochastic Differential Equations, Sudip Sinha
Anticipating Stochastic Integrals And Related Linear Stochastic Differential Equations, Sudip Sinha
LSU Doctoral Dissertations
Itô’s stochastic calculus revolutionized the field of stochastic analysis and has found numerous applications in a wide variety of disciplines. Itô’s theory, even though quite general, cannot handle anticipating stochastic processes as integrands. There have been considerable efforts within the mathematical community to extend Itô’s calculus to account for anticipation. The Ayed–Kuo integral — introduced in 2008 — is one of the most recent developments. It is arguably the most accessible among the theories extending Itô’s calculus — relying solely on probabilistic methods. In this dissertation, we look at the recent advances in this area, highlighting our contributions. First, we …
A New Perspective On A Polynomial Time Knot Polynomial, Robert John Quarles
A New Perspective On A Polynomial Time Knot Polynomial, Robert John Quarles
LSU Doctoral Dissertations
In this work we consider the Z1(K) polynomial time knot polynomial defined and
described by Dror Bar-Natan and Roland van der Veen in their 2018 paper ”A polynomial time knot polynomial”. We first look at some of the basic properties of Z1(K), and develop an invariant of diagrams Ψm(D) related to this polynomial. We use this invariant as a model to prove how Z1(K) acts under the connected sum operation. We then discuss the effect of mirroring the knot on Z1(K), and described a geometric interpretation of some of the building blocks of the invariant. We then use these to …
General Stochastic Calculus And Applications, Pujan Shrestha
General Stochastic Calculus And Applications, Pujan Shrestha
LSU Doctoral Dissertations
In 1942, K. Itô published his pioneering paper on stochastic integration with respect to Brownian motion. This work led to the framework for Itô calculus. Note that, Itô calculus is limited in working with knowledge from the future. There have been many generalizations of the stochastic integral in being able to do so. In 2008, W. Ayed and H.-H. Kuo introduced a new stochastic integral by splitting the integrand into the adaptive part and the counterpart called instantly independent. In this doctoral work, we conduct deeper research into the Ayed–Kuo stochastic integral and corresponding anticipating stochastic calculus.
We provide a …
Characterizations Of Certain Classes Of Graphs And Matroids, Jagdeep Singh
Characterizations Of Certain Classes Of Graphs And Matroids, Jagdeep Singh
LSU Doctoral Dissertations
``If a theorem about graphs can be expressed in terms of edges and cycles only, it probably exemplifies a more general theorem about matroids." Most of my work draws inspiration from this assertion, made by Tutte in 1979.
In 2004, Ehrenfeucht, Harju and Rozenberg proved that all graphs can be constructed from complete graphs via a sequence of the operations of complementation, switching edges and non-edges at a vertex, and local complementation. In Chapter 2, we consider the binary matroid analogue of each of these graph operations. We prove that the analogue of the result of Ehrenfeucht et. al. does …
Unavoidable Structures In Large And Infinite Graphs, Sarah Allred
Unavoidable Structures In Large And Infinite Graphs, Sarah Allred
LSU Doctoral Dissertations
In this work, we present results on the unavoidable structures in large connected and large 2-connected graphs. For the relation of induced subgraphs, Ramsey proved that for every positive integer r, every sufficiently large graph contains as an induced subgraph either Kr or Kr. It is well known that, for every positive integer r, every sufficiently large connected graph contains an induced subgraph isomorphic to one of Kr, K1,r, and Pr. We prove an analogous result for 2-connected graphs. Similarly, for infinite graphs, every infinite connected graph contains an induced subgraph …
Gl(1|1) Graph Connections, Andrea Bourque
Opers On The Projective Line, Wronskian Relations, And The Bethe Ansatz, Ty J. Brinson
Opers On The Projective Line, Wronskian Relations, And The Bethe Ansatz, Ty J. Brinson
Honors Theses
No abstract provided.
Spectral Theorem Approach To The Characteristic Function Of Quantum Observables, Andreas Boukas
Spectral Theorem Approach To The Characteristic Function Of Quantum Observables, Andreas Boukas
Journal of Stochastic Analysis
No abstract provided.