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

    Hu, Yaozhong; Liu, Yanghui; Nualart, David (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 

    Corwin, Ivan; Liu, Zhipeng; Wang, Dong (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 

    Quas, Anthony; Soo, Terry (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 

    Nourdin, Ivan; Nualart, David; Peccati, Giovanni (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 

    Hu, Yaozhong; Huang, Jingyu; Nualart, David (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 

    Huang, Weizhang; Kamenski, Lennard; Lang, Jens (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 

    Duval, Art; Klivans, Caroline; Martin, Jeremy L. (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 

    Cook, George Stafford (University of Kansas, 1930)
  • Multiplicities in Commutative Algebra 

    Serio, Jared Grant (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 

    Brune, Peter R.; Knepley, Matthew G.; Smith, Barry F.; Tu, Xuemin (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 ...

    Tu, Xuemin; Li, Jing (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 

    Kwon, Soonsik; Shao, Shuanglin (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 

    Deya, Aurelien; Nualart, David; Tindel, Samy (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 

    Hu, Yaozhong; Huang, Jingyu; Nualart, David; Tindel, Samy (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 

    Hu, Yaozhong; Nualart, David; Tindel, Samy; Xu, Fangjun (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 

    Ji, Shuguan; Liu, Weishi; Zhang, Mingji (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 

    Hur, Vera Mikyoung; Johnson, Mathew A. (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 

    Mallonee, Pauline Virginia (University of Kansas, 1929)
  • Application of stochastic differential equations to option pricing 

    Wang, Peixin (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 

    Su, Chen (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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