Browsing EPrint Collection  Mathematics by Author "Chen, ZhenQing"
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Censored stable processes
Burdzy, Krzysztof; Bogdan, Krzysztof; Chen, ZhenQing (SpringerVerlag GmbH, 200309)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, ZhenQing (SpringerVerlag GmbH, 200208)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, ZhenQing (2005)We discuss the relationships between the notion of intrinsic ultracontractivity, parabolic Harnack principle, compactness of the 1resolvent of the Neumann Laplacian, and nontrap property for Euclidean domains with finite ... 
The Heat Equation and Reflected Brownian Motion in TimeDependent Domains
Burdzy, Krzysztof; Chen, ZhenQing; Sylvester, John (Institute of Mathematical Statistics, 200401)The paper is concerned with reflecting Brownian motion (RBM) in domains with deterministic moving boundaries, also known as "noncylindrical domains," and its connections with partial differential equations. Construction ... 
The heat equation in time dependent domains with insulated boundaries
Burdzy, Krzysztof; Chen, ZhenQing; Sylvester, John (Academic Press (Elsevier), 200410)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, ZhenQing (Institute of Mathematical Statistics, 200110)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, ZhenQing (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, ZhenQing (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, ZhenQing (NorthHolland (Elsevier), 200405)Let Z [subscript] t be a onedimensional 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, ZhenQing; 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, ZhenQing; Marshall, Donald E. (SpringerVerlag GmbH, 20050816)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, ZhenQing (Elsevier, 200503)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, ZhenQing (Institute of Mathematical Statistics, 19980523)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. ...