Now showing items 1-13 of 13

    • Censored stable processes 

      Burdzy, Krzysztof; Bogdan, Krzysztof; Chen, Zhen-Qing (Springer-Verlag GmbH, 2003-09)
      We present several constructions of a "censored stable process" in an open set D [is an element of the subset] R [to the power of] n, i.e., a symmetric stable process which is not allowed to jump outside D. We address ...
    • Coalescence of synchronous couplings 

      Burdzy, Krzysztof; Chen, Zhen-Qing (Springer-Verlag GmbH, 2002-08)
      We consider a pair of reflected Brownian motions in a Lipschitz planar domain starting from different points but driven by the same Brownian motion. First we construct such a pair of processes in a certain weak sense, since ...
    • Comparison of potential theoretic properties of rough domains 

      Burdzy, Krzysztof; Chen, Zhen-Qing (2005)
      We discuss the relationships between the notion of intrinsic ultracontractivity, parabolic Harnack principle, compactness of the 1-resolvent of the Neumann Laplacian, and non-trap property for Euclidean domains with finite ...
    • The Heat Equation and Reflected Brownian Motion in Time-Dependent Domains 

      Burdzy, Krzysztof; Chen, Zhen-Qing; Sylvester, John (Institute of Mathematical Statistics, 2004-01)
      The paper is concerned with reflecting Brownian motion (RBM) in domains with deterministic moving boundaries, also known as "non-cylindrical domains," and its connections with partial differential equations. Construction ...
    • The heat equation in time dependent domains with insulated boundaries 

      Burdzy, Krzysztof; Chen, Zhen-Qing; Sylvester, John (Academic Press (Elsevier), 2004-10)
      The paper studies, among other things, two types of possible singularities of the solution to the heat equation at the boundary of a moving domain. Several explicit results on "heat atoms" and "heat singularities" are given.
    • Local time flow related to skew Brownian motion 

      Burdzy, Krzysztof; Chen, Zhen-Qing (Institute of Mathematical Statistics, 2001-10)
      We define a local time flow of skew Brownian motions, i.e., a family of solutions to the stochastic differential equation defining the skew Brownian motion, starting from different points but driven by the same Brownian ...
    • On the Robin problem in fractal domains 

      Bass, Richard F.; Burdzy, Krzysztof; Chen, Zhen-Qing (2005)
      We study the solution to the Robin boundary problem for the Laplacian in a Euclidean domain. We present some families of fractal domains where the infimum is greater than 0, and some other families of domains where it is ...
    • Shy Couplings 

      Benjamini, Itai; Burdzy, Krzysztof; Chen, Zhen-Qing (2005)
      A pair (X; Y) of Markov processes is called a Markov coupling if X and Y have the same transition probabilities and (X;Y) is a Markov process. We say that a coupling is "shy" if there exists a (random) [Epsilon] > 0 such ...
    • Stochastic differential equations driven by stable processes for which pathwise uniqueness fails 

      Burdzy, Krzysztof; Bass, Richard F.; Chen, Zhen-Qing (North-Holland (Elsevier), 2004-05)
      Let Z [subscript] t be a one-dimensional symmetric stable process of order [alpha] with [alpha is an element of the set] (0, 2) and consider the stochastic differential equation dX [subscript] t = [omega] (X [subscript] ...
    • Synchronous couplings of reflected Brownian motions in smooth domains 

      Burdzy, Krzysztof; Chen, Zhen-Qing; Jones, Peter (2005)
      For every bounded planar domain D with a smooth boundary, we define a "Lyapunov exponent" [Lambda](D) using a fairly explicit formula. We consider two reflected Brownian motions in D, driven by the same Brownian motion ...
    • Traps for Reflected Brownian Motion 

      Burdzy, Krzysztof; Chen, Zhen-Qing; Marshall, Donald E. (Springer-Verlag GmbH, 2005-08-16)
      Consider an open set D [is an element of the set] R [The set of Real Numbers] [superscript]d, d [is greater than or equal to] 2, and a closed ball B [is a proper subset of] D. Let E[superscript]xT[subscript]B denote the ...
    • Uniqueness for reflecting Brownian motion in lip domains 

      Burdzy, Krzysztof; Bass, Richard F.; Chen, Zhen-Qing (Elsevier, 2005-03)
      A lip domain is a Lipschitz domain where the Lipschitz constant is strictly less than one. We prove strong existence and pathwise uniqueness for the solution X = {X [subscript] t, t [is less than or equal to] 0} to the ...
    • Weak convergence of reflecting Brownian motions 

      Burdzy, Krzysztof; Chen, Zhen-Qing (Institute of Mathematical Statistics, 1998-05-23)
      We will show that if a sequence of domains D [subscript] k increases to a domain D then the reflected Brownian motions in D [subscript] k's converge to the reflected Brownian motion in D, under mild technical assumptions. ...