Now showing items 93-112 of 112

    • 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 ...
    • A Skorobod-type lemma and a decomposition of reflected Brownian motion 

      Burdzy, Krzysztof; Toby, Ellen H. (Institute of Mathematical Statistics, 1995-04)
      We consider two-dimensional reflected Brownian motions in sharp thorns pointed downward with horizontal vectors of reflection. We present a decomposition of the process into a Brownian motion and a process which has bounded ...
    • Small triangle-free configurations of points and lines 

      Boben, Marko; Grünbaum, Branko; Pisanski, Tomaz; Zitnik, Arjana (2006)
      In this paper we show that all combinatorial triangle-free configurations (v_3) for v (is less than or equal to) 8 are geometrically realizable. We also show that there is a unique smallest astral (18_3) triangle-free ...
    • Some path properties of iterated Brownian motion 

      Burdzy, Krzysztof (Birkhauser Boston, Inc., 1993)
      The present paper is devoted to studying path properties of iterated Brownian motion (IBM). We want to examine how the lack of independence of increments influences the results and estimates which are well understood in ...
    • Stable processes have thorns 

      Burdzy, Krzysztof; Kulczycki, Tadeusz (Institute of Mathematical Statistics, 2003-01)
      Let X(t) be the symmetric [alpha]-stable process in R [to the power of] d, [alpha is an element of the set] (0, 2), d [is greater than or equal to] 2. For f : (0, 1) [approaching] (0,[infinity]) let D(f) be the thorn {x ...
    • Stochastic bifurcation models 

      Burdzy, Krzysztof; Bass, Richard F. (Institute of Mathematical Statistics, 1999-01)
      We study an ordinary differential equation controlled by a stochastic process. We present results on existence and uniqueness of solutions, on associated local times (Trotter and Ray-Knight theorems), and on time and ...
    • 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] ...
    • Super-Brownian motion with reflecting historical paths 

      Burdzy, Krzysztof; Le Gall, Jean-Francois (Springer-Verlag GmbH, 2001-12)
      We consider super-Brownian motion whose historical paths reflect from each other, unlike those of the usual historical super-Brownian motion. We prove tightness for the family of distributions corresponding to a sequence ...
    • Super-Brownian motion with reflecting historical paths. II: Convergence of approximations 

      Burdzy, Krzysztof; Mytnik, Leonid (Springer-Verlag GmbH, 2005-10)
      We prove that the sequence of finite reflecting branching Brownian motion forests defined by Burdzy and Le Gall ([?]) converges in probability to the "super-Brownian motion with reflecting historical paths." This solves ...
    • The supremum of Brownian local times on Holder curves 

      Burdzy, Krzysztof; Bass, Richard F. (Elsevier, 2001-11)
      For f : [maps the set] [0, 1] [into the set of real numbers] R, we consider L ([to the power of] f [subscript] t), the local time of spacetime Brownian motion on the curve f. Let S [subscript alpha] be the class of all ...
    • 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 ...
    • A three-dimensional Brownian path reflected on a Brownian path is a free Brownian path 

      Burdzy, Krzysztof (Springer Science+Business Media B.V., 1993)
      Three-dimensional Brownian path reflected on Brownian path is a free Brownian path.
    • Topics in Topology and Homotopy Theory 

      Warner, Garth (Hopf Topology Archive, 2005-01)
      This book is addressed to those readers who have been through Rotman (or its equivalent), possess a wellthumbed copy of Spanier, and have a good background in algebra and general topology. Granted these prerequisites, ...
    • 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 ...
    • Unsolved Problems in Intuitive Geometry 

      Klee, Victor (1960)
    • Variably skewed Brownian motion 

      Burdzy, Krzysztof; Barlow, Martin T.; Kaspi, Haya; Mandelbaum, Avi (Institute of Mathematical Statistics, 2000-03-01)
      Given a standard Brownian motion B, we show that the equation X [subscript] t = x [subscript] 0 + B [subscript] t + [beta](L [to the power of X] [subscript] t ); t [is greater than or equal to] 0 ; has a unique strong ...
    • Variation of iterated Brownian motion 

      Burdzy, Krzysztof (American Mathematical Society, 1994)
      In this paper, we study higher order variations of iterated Brownian motion (IBM) with view towards possible applications to the construction of the stochastic integral with respect to IBM. We prove that the 4-th variation ...
    • 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. ...
    • What symmetry groups are present in the Alhambra? 

      Grünbaum, Branko (American Mathematical Society, 2006)
      The question which of the seventeen wallpaper groups are represented in the fabled ornamentation of the Alhambra has been raised and discussed quite often, with widely diverging answers. Some of the arguments from these ...