### Recent Submissions

• #### Rate of convergence and asymptotic error distribution of Euler approximation schemes for fractional diffusions ﻿

(American Meteorological Society, 2016-03-22)
For a stochastic differential equation(SDE) driven by a fractional Brownian motion(fBm) with Hurst parameter H>12, it is known that the existing (naive) Euler scheme has the rate of convergence n1−2H. Since the limit H→12 ...
• #### Fluctuations of TASEP and LPP with general initial data ﻿

(Institute of Mathematical Statistics, 2015-08-13)
We prove Airy process variational formulas for the one-point probability distribution of (discrete time parallel update) TASEP with general initial data, as well as last passage percolation from a general lattice path to ...
• #### A monotone Sinai theorem ﻿

(Institute of Mathematical Statistics, 2016-02-02)
Sinai proved that a nonatomic ergodic measure-preserving system has any Bernoulli shift of no greater entropy as a factor. Given a Bernoulli shift, we show that any other Bernoulli shift that is of strictly less entropy ...
• #### Quantitative stable limit theorems on the Wiener space ﻿

(Institute of Mathematical Statistics, 2016)
We use Malliavin operators in order to prove quantitative stable limit theorems on the Wiener space, where the target distribution is given by a possibly multidimensional mixture of Gaussian distributions. Our findings ...
• #### On the intermittency front of stochastic heat equation driven by colored noises ﻿

(Institute of Mathematical Statistics, 2016-03-01)
We study the propagation of high peaks (intermittency fronts) of the solution to a stochastic heat equation driven by multiplicative centered Gaussian noise in RdRd. The noise is assumed to have a general homogeneous ...
• #### Stability of Explicit One-Step Methods for P1-Finite Element Approximation of Linear Diffusion Equations on Anisotropic Meshes ﻿

(Society for Industrial and Applied Mathematics, 2016-05-26)
We study the stability of explicit one-step integration schemes for the linear finite element approximation of linear parabolic equations. The derived bound on the largest permissible time step is tight for any mesh and ...
• #### The Partitionability Conjecture ﻿

(American Mathematical Society, 2017-02)
In 1979 Richard Stanley made the following conjecture: Every Cohen-Macaulay simplicial complex is partitionable. Motivated by questions in the theory of face numbers of simplicial complexes, the Partitionability Conjecture ...
• #### Certain plane configurations ﻿

(University of Kansas, 1930)
• #### Multiplicities in Commutative Algebra ﻿

(University of Kansas, 2016-08-31)
This dissertation explores the notion of multiplicity and its generalizations within the theory of commutative algebra. Chapter 2 is dedicated to calculating the limits which give rise to Buchsbaum-Rim multiplicities. We ...
• #### Composing Scalable Nonlinear Algebraic Solvers ﻿

(Society for Industrial and Applied Mathematics (SIAM), 2015-11-05)
Most efficient linear solvers use composable algorithmic components, with the most common model being the combination of a Krylov accelerator and one or more preconditioners. A similar set of concepts may be used for ...
• #### A FETI-DP TYPE DOMAIN DECOMPOSITION ALGORITHM FOR THREE-DIMENSIONAL INCOMPRESSIBLE STOKES EQUATIONS ﻿

(Society for Industrial and Applied Mathematics, 2015-03-03)
The FETI-DP (dual-primal finite element tearing and interconnecting) algorithms, proposed by the authors in [SIAM J. Numer. Anal., 51 (2013), pp. 1235–1253] and [Internat. J. Numer. Methods Engrg., 94 (2013), pp. 128–149] ...
• #### Nonexistence of soliton-like solutions for defocusing generalized KdV equations ﻿

(Texas State University, Department of Mathematics, 2015-02-24)
We consider the global dynamics of the defocusing generalized KdV equation $$\partial_t u + \partial_x^3 u = \partial_x(|u|^{p-1}u).$$ We use Tao's theorem [5] that the energy moves faster than the mass to prove a ...
• #### On L2 modulus of continuity of Brownian local times and Riesz potentials ﻿

(Institute of Mathematical Statistics, 2015-05-05)
This article is concerned with modulus of continuity of Brownian local times. Specifically, we focus on three closely related problems: (a) Limit theorem for a Brownian modulus of continuity involving Riesz potentials, ...
• #### Stochastic heat equations with general multiplicative Gaussian noises: Hölder continuity and intermittency ﻿

(Institute of Mathematical Statistics, 2016-06-04)
This paper studies the stochastic heat equation with multiplicative noises of the form uW, where W is a mean zero Gaussian noise and the differential element uW is interpreted both in the sense of Skorohod and Stratonovich. ...
• #### Density convergence in the Breuer-Major theorem for Gaussian stationary sequences ﻿

(Bernoulli Society for Mathematical Statistics and Probability, 2015)
Consider a Gaussian stationary sequence with unit variance X={Xk;k∈N∪{0}}. Assume that the central limit theorem holds for a weighted sum of the form Vn=n−1/2∑n−1k=0f(Xk), where f designates a finite sum of Hermite ...
• #### Effects of (Small) Permanent Charge and Channel Geometry on Ionic Flows via Classical Poisson--Nernst--Planck Models ﻿

(Society for Industrial and Applied Mathematics, 2015-01-15)
In this work, we examine effects of permanent charges on ionic flows through ion channels via a quasi-one-dimensional classical Poisson--Nernst--Planck (PNP) model. The geometry of the three-dimensional channel is presented ...
• #### Stability of Periodic Traveling Waves for Nonlinear Dispersive Equations ﻿

(Society for Industrial and Applied Mathematics, 2015-09-17)
We study the stability and instability of periodic traveling waves for Korteweg--de Vries-type equations with fractional dispersion and related, nonlinear dispersive equations. We show that a local constrained minimizer ...
• #### On summation of finite series ﻿

(University of Kansas, 1929)
• #### Application of stochastic differential equations to option pricing ﻿

(University of Kansas, 2016-05-31)
The financial world is a world of random things and unpredictable events. Along with the innovative development of diversity and complexity in modern financial market, there are more and more financial derivative emerged ...
• #### Some Studies on Parameter Estimations ﻿

(University of Kansas, 2016-05-31)
Parameter estimation has wide applications in such fields as finance, biological science, weather prediction, oil deposit detection, etc. Researchers are particularly interested in reconstructing some unknown parameters ...

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KU Libraries
1425 Jayhawk Blvd
Lawrence, KS 66045