Browsing Mathematics, Department of by Author "Burdzy, Krzysztof"

Now showing items 21-40 of 84

    • Efficient Markovian couplings: Examples and counterexamples 

      Burdzy, Krzysztof; Kendall, Wilfrid S. (Institute of Mathematical Statistics, 2000-05)
      In this paper we study the notion of an efficient coupling of Markov processes. Informally, an efficient coupling is one which couples at the maximum possible exponential rate, as given by the spectral gap. This notion ...

    • Eigenvalue expansions for Brownian motion with an application to occupation times 

      Burdzy, Krzysztof; Bass, Richard F. (Institute of Mathematical Statistics, 1996-01-31)
      Let B be a Borel subset of R [to the power of] d with finite volume. We give an eigenvalue expansion for the transition densities of Brownian motion killed on exiting B. Let A [subscript] 1 be the time spent by Brownian ...

    • Erratum to The Supremum of Brownian Times on Hölder Curves 

      Bass, Richard F.; Burdzy, Krzysztof (Birkhauser, 2002-05-21)
      For [function] f [maps the set]: [0, 1] [into the set] [Real numbers], we consider L [superscript] f [subscript] t , the local time of spacetime Brownian motion on the curve f. Let S [subscript][sigma] be the class of all ...

    • Excursion laws and exceptional points on Brownian paths 

      Burdzy, Krzysztof (Springer-Verlag, 1993)
      The purpose of this note is to present an example of a family of "exceptional points" on Brownian paths which cannot be constructed using an entrance law.

    • Fast equilibrium selection by rational players living in a changing world 

      Burdzy, Krzysztof; Frankel, David M.; Pauzner, Ady (The Econometric Society, 2001-01)
      We study a coordination game with randomly changing payoffs and small frictions in changing actions. Using only backwards induction, we find that players must coordinate on the risk-dominant equilibrium. More precisely, a ...

    • Fiber Brownian motion and the "hot spots" problem 

      Burdzy, Krzysztof; Bass, Richard F. (Duke University Press, 2000-10)
      We show that in some planar domains both extrema of the second Neumann eigenfunction lie strictly inside the domain. The main technical innovation is the use of "fiber Brownian motion," a process which switches between ...

    • A Fleming-Viat particle representation of Dirichlet Laplacian 

      Burdzy, Krzysztof; Holyst, Robert; March, Peter (Springer-Verlag GmbH, 2000-11)
      We consider a model with a large number N of particles which move according to independent Brownian motions. A particle which leaves a domain D is killed; at the same time, a different particle splits into two particles. ...

    • A Gaussian oscillator 

      Burdzy, Krzysztof; White, David (Institute of Mathematical Statistics, 2004-10-06)
      We present a stochastic process with sawtooth paths whose distribution is given by a simple rule and whose stationary distribution is Gaussian. The process arose in a natural way in research on interaction of an inert ...

    • Geometric Properties of 2-dimensional Brownian Paths 

      Burdzy, Krzysztof (Springer-Verlag GmbH, 1989)
      Let A be the set of all points of the plane C, visited by two-dimensional Brownian motion before time 1. With probability 1, all points of A are "twist points" except a set of harmonic measure zero. "Twist points" may be ...

    • 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.

    • Hitting a boundary point with reflected Brownian motion 

      Burdzy, Krzysztof; Marshall, Donald E. (Springer-Verlag, 1992)
      An explicit integral test involving the reflection angle is given for the reflected Brownian motion in a half-plane to hit a fixed boundary point.

    • The "hot spots" problem in planar domains with one hole. 

      Burdzy, Krzysztof (Duke University Press, 2005)
      There exists a planar domain with piecewise smooth boundary and one hole such that the second eigenfunction for the Laplacian with Neumann boundary conditions attains its maximum and minimum inside the domain.

    • Hölder domains and the boundary Harnack principle 

      Banuelos, Rodrigo; Bass, Richard F.; Burdzy, Krzysztof (Duke University Press, 1991-10)
      A version of the boundary Harnack principle is proven.

    • Intersection local time for points of infinite multiplicity 

      Burdzy, Krzysztof; Bass, Richard F.; Khoshnevisan, Davar (Institute of Mathematical Statistics, 1994-04)
      For each a [is an element of the set] (0, 1/2), there exists a random measure [beta] [subscript] a which is supported on the set of points where two-dimensional Brownian motion spends a units of local time. The measure ...

    • Iterated law of iterated logarithm 

      Burdzy, Krzysztof; San Martin, Jaime (Institute of Mathematical Statistics, 1995-10)
      Suppose [epsilon] [is a member of the set] [0, 1) and let theta [subscipt epsilon] (t) = (1 − [epsilon]) [square root of] (2tln [subscript] 2 t). Let L [to the power of epsilon] [subscript] t denote the amount of local ...

    • Ito formula for an asymptotically 4-stable process 

      Burdzy, Krzysztof; Madrecki, Andrzej (Institute of Mathematical Statistics, 1996-02)
      An Ito-type formula is given for an asymptotically 4-stable process.

    • Labyrinth dimension of Brownian trace 

      Burdzy, Krzysztof (Institute of Mathematics, 1995)
      Suppose that X is a two-dimensional Brownian motion. The trace X[0, 1] contains a self-avoiding continuous path whose Hausdorff dimension is equal to 2.

    • Lenses in skew Brownian flow 

      Burdzy, Krzysztof; Kaspi, Haya (Institute of Mathematical Statistics, 2004-10)
      We consider a stochastic flow in which individual particles follow skew Brownian motions, with each one of these processes driven by the same Brownian motion. One does not have uniqueness for the solutions of the corresponding ...

    • The level sets of iterated Brownian motion 

      Burdzy, Krzysztof; Khoshnevisan, Davar (Springer-Verlag, 1995)
      We show that the Hausdorff dimension of every level set of iterated Brownian motion is equal to 3/4.