ResearchWorks Archive

Browsing EPrint Collection - Mathematics by Title

Browsing EPrint Collection - Mathematics by Title

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  • Burdzy, Krzysztof; Frankel, David M. (Berkeley Electronic Press, 2005)
    A popular theory of business cycles is that they are driven by animal spirits: shifts in expectations brought on by sunspots. A prominent example is Howitt and McAfee (AER, 1992). We show that this model has a unique ...
  • Frankel, David M.; Burdzy, Krzysztof (2005)
    A popular theory of business cycles is that they are driven by animal spirits: shifts in expectations brought on by sunspots. A prominent example is Howitt and McAfee (AER, 1992). We show that this model has a unique ...
  • 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 ...
  • 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 ...
  • 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 ...
  • 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 ...
  • 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 ...
  • 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 ...
  • 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] ...
  • 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 ...
  • 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 ...
  • 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 ...
  • 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 ...
  • Burdzy, Krzysztof (Springer Science+Business Media B.V., 1993)
    Three-dimensional Brownian path reflected on Brownian path is a free Brownian path.
  • 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, ...
  • 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 ...
  • 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 ...
  • Klee, Victor (1960)
  • 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 ...
  • 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 ...

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