Mathematics Commons^™

An Anti-Symmetric Version Of Malliavin Calculus, Jirô Akahori, Tomo Matsusita, Yasufumi Nitta

Journal of Stochastic Analysis

No abstract provided.

Transfer Of Regularity For Markov Semigroups By Using An Interpolation Technique, Vlad Bally, Lucia Caramellino

Journal of Stochastic Analysis

No abstract provided.

Integration By Parts Formula On Solutions To Stochastic Differential Equations With Jumps On Riemannian Manifolds, Hirotaka Kai, Atsushi Takeuchi

Journal of Stochastic Analysis

No abstract provided.

On The Exponential Moments Of Additive Processes, Tsukasa Fujiwara

Journal of Stochastic Analysis

No abstract provided.

Ergodicity Of Burgers' System, Szymon Peszat, Krystyna Twardowska, Jerzy Zabczyk

Journal of Stochastic Analysis

No abstract provided.

Two Of Kunita's Papers On Stochastic Flows In Early 1980s, Setsuo Taniguchi

Journal of Stochastic Analysis

No abstract provided.

Rigid Connections On The Projective Line With Elliptic Toral Singularities, Alisina Azhang

LSU Doctoral Dissertations

We generalize two studies of rigid $G$-connections on $\pp$ which have an irregular singularity at origin and a regular singularity at infinity with unipotent monodromy: one is the work of Kamgarpour-Sage which classifies rigid homogeneous Coxeter $G$-connections with slope $\frac{r}{h}$, where $h$ is the Coxeter number of $G$, and the other is the work of Chen, which proves the existence of rigid homogeneous elliptic regular $G$-connections with slope $\frac{1}{m}$, where $m$ is an elliptic number for $G$. In our work, similar to Chen, we look for rigid homogeneous elliptic regular $G$-connections, but we allow the slope to have a numerator …

Error Estimates For Discrete Approximations Of Game Options With Multivariate Diffusion Asset Prices, Yuri Kifer

Journal of Stochastic Analysis

No abstract provided.

Hessian Formulas And Estimates For Parabolic Schrödinger Operators, Xue-Mei Li

Journal of Stochastic Analysis

No abstract provided.

Remembering Kunita-San, Ken-Iti Sato

Journal of Stochastic Analysis

No abstract provided.

The Life And Scientific Work Of Hiroshi Kunita, Yasushi Ishikawa

Journal of Stochastic Analysis

No abstract provided.

Memories Of Professor Hiroshi Kunita, Ichiro Shigkeawa

Journal of Stochastic Analysis

No abstract provided.

On The Works Of Hiroshi Kunita In The Sixties, Masatoshi Fukushima

Journal of Stochastic Analysis

No abstract provided.

Personal Memories Of Hiroshi Kunita, David Elworthy

Journal of Stochastic Analysis

No abstract provided.

Preface, Shigeki Aida, David Applebaum, Yasushi Ishikawa, Arturo Kohatsu-Higa, Nicolas Privault

Journal of Stochastic Analysis

No abstract provided.

Algorithms Related To Triangle Groups, Bao The Pham

LSU Doctoral Dissertations

Given a finite index subgroup of $\PSL_2(\Z)$, one can talk about the different properties of this subgroup. These properties have been studied extensively in an attempt to classify these subgroups. Tim Hsu created an algorithm to determine whether a subgroup is a congruence subgroup by using permutations \cite{hsu}. Lang, Lim, and Tan also created an algorithm to determine if a subgroup is a congruence subgroup by using Farey Symbols \cite{llt}. Sebbar classified torsion-free congruence subgroups of genus 0 \cite{sebbar}. Pauli and Cummins computed and tabulated all congruence subgroups of genus less than 24 \cite{ps}. However, there are still some problems …

Berry-Esseen Bounds For Approximate Maximum Likelihood Estimators In The Α-Brownian Bridge, Khalifa Es-Sebaiy, Jabrane Moustaaid, Idir Ouassou

Journal of Stochastic Analysis

No abstract provided.

Numeric And Dynamic B-Stability, Exact-Monotone And Asymptotic Two-Point Behavior Of Theta Methods For Stochastic Differential Equations, Henri Schurz

Journal of Stochastic Analysis

No abstract provided.

An Equivalence Between Contact Gluing Maps In Sutured Floer Homology: A Conjecture Of Zarev, Charles Ryan Leigon

LSU Doctoral Dissertations

We show that the contact gluing map of Honda, Kazez, and Matic has a natural algebraic description in bordered sutured Floer homology. In particular, we establish Zarev's conjecture that his gluing map on sutured Floer homology is equivalent, in the appropriate sense, to the contact gluing map. This further solidifies the relationship between bordered Floer theory and contact geometry.

On Distributions Of Self-Adjoint Extensions Of Symmetric Operators, Franco Fagnola, Zheng Li

Journal of Stochastic Analysis

No abstract provided.

Noncommutative Tensor Triangular Geometry And Its Applications To Representation Theory, Kent Barton Vashaw

LSU Doctoral Dissertations

One of the cornerstones of the representation theory of Hopf algebras and finite tensor categories is the theory of support varieties. Balmer introduced tensor triangular geometry for symmetric monoidal triangulated categories, which united various support variety theories coming from disparate areas such as homotopy theory, algebraic geometry, and representation theory. In this thesis a noncommutative version will be introduced and developed. We show that this noncommutative analogue of Balmer's theory can be determined in many concrete situations via the theory of abstract support data, and can be used to classify thick tensor ideals. We prove an analogue of prime ideal …

Anticipating Linear Stochastic Differential Equations With Adapted Coefficients, Hui-Hsiung Kuo, Pujan Shrestha, Sudip Sinha

Journal of Stochastic Analysis

No abstract provided.

On Properties Of Weil Sums Of Binomials, Liem P. Nguyen

LSU Doctoral Dissertations

This dissertation explores questions regarding the Weil sum of binomials, a finite field character sum originated from information theory. The Weil spectrum counts distinct values of the Weil sum through invertible elements in the finite field. The value of these sums and the size of the Weil spectrum are of particular interest, as they link problems in information theory, coding theory, and cryptography to other areas of math such as number theory and arithmetic geometry. In the setting of Niho exponents, we prove the Vanishing Conjecture of Helleseth ($1971$) on the presence of zero values in the Weil spectrum and …

Applications Of Nonstandard Analysis In Probability And Measure Theory, Irfan Alam

LSU Doctoral Dissertations

This dissertation broadly deals with two areas of probability theory and investigates how methods from nonstandard analysis may provide new perspectives in these topics. In particular, we use nonstandard analysis to prove new results in the topics of limiting spherical integrals and of exchangeability.

In the former area, our methods allow us to represent finite dimensional Gaussian measures in terms of marginals of measures on hyperfinite-dimensional spheres in a certain strong sense, thus generalizing some previously known results on Gaussian Radon transforms as limits of spherical integrals. This first area has roots in the kinetic theory of gases, which is …

The Edwards Model For Fractional Brownian Loops And Starbursts, Wolfgang Bock, Torben Fattler, Ludwig Streit

Journal of Stochastic Analysis

No abstract provided.

Alòs Type Decomposition Formula For Barndorff-Nielsen And Shephard Model, Takuji Arai

Journal of Stochastic Analysis

No abstract provided.

Mixed Generalized Fractional Brownian Motion, Shaykhah Alajmi, Ezzedine Mliki

Journal of Stochastic Analysis

No abstract provided.

Exact Solutions To Optimal Control Problems For Wiener Processes With Exponential Jumps, Mario Lefebvre

Journal of Stochastic Analysis

No abstract provided.

Dna Curve Classification With Unsupervised Learning, Ben Thomas

Honors Capstones

No abstract provided.

Connectivity Of Matroids And Polymatroids, Zachary R. Gershkoff

LSU Doctoral Dissertations

This dissertation is a collection of work on matroid and polymatroid connectivity. Connectivity is a useful property of matroids that allows a matroid to be decomposed naturally into its connected components, which are like blocks in a graph. The Cunningham-Edmonds tree decomposition further gives a way to decompose matroids into 3-connected minors. Much of the research below concerns alternate senses in which matroids and polymatroids can be connected. After a brief introduction to matroid theory in Chapter 1, the main results of this dissertation are given in Chapters 2 and 3. Tutte proved that, for an element e of a …