Now showing items 1-20 of 32

    • 2-D Brownian motion in a system of reflecting barriers: effective diffusivity by a sampling method 

      Burdzy, Krzysztof; Holyst, Robert; Ingerman, David (Institute of Physics, 1994-02-07)
      We study two-dimensional Brownian motion in an ordered periodic system of linear reflecting barriers using the sampling method and conformal transformations. We calculate the effective diffusivity for the Brownian particle. ...
    • 2-D Brownian motion in a system of traps: Application of conformal transformations 

      Burdzy, Krzysztof; Holyst, Robert; Salisbury, Thomas S. (Institute of Physics, 1992)
      We study two-dimensional Brownian motion in a periodic system of traps using conformal transformations. The system is periodic in the x and y directions. We calculate the ratio of the drift along the y-axis to the drift ...
    • An asymptotically 4-stable process 

      Burdzy, Krzysztof; Madrecki, Andrzej (CRC Press, 1995)
      An asymptotically 4-stable process is constructed. The model identifies the 4-stable process with a sequence of processes converging in a very weak sense. It is proved that the 4-th variation of the process is a linear ...
    • Brownian motion reflected on Brownian motion 

      Burdzy, Krzysztof; Nualart, David (Springer-Verlag GmbH, 2002-04)
      We study Brownian motion reflected on an "independent" Brownian path. We prove results on the joint distribution of both processes and the support of the parabolic measure in the space-time domain bounded by a Brownian ...
    • A critical case for Brownian slow points 

      Burdzy, Krzysztof; Bass, Richard F. (Springer-Verlag GmbH, 1996-01)
      Let X [subscript] t be a Brownian motion and let S(c) be the set of reals r [is greather than or equal to] 0 such that |X ([subscript] r+t) − X [subscript] r| [is less than or equal to] c [square root of] t, 0 [is less ...
    • Curvature of the convex hull of planar Brownian motion near its minimum point 

      Burdzy, Krzysztof; San Martin, Jaime (North-Holland (Elsevier), 1989-10)
      Let f be a (random) real-valued function whose graph represents the boundary of the convex hull of planar Brownian motion run until time 1 near its lowest point in a coordinate system so that f is non-negative and f(0) = ...
    • Cut points on Brownian paths 

      Burdzy, Krzysztof (Institute of Mathematical Statistics, 1989-07)
      Let X be a standard two-dimensional Brownian motion. There exists a.s. t [is an element of the set] (0; 1) such that X([0; t))[intersected with] X((t; 1]) = [empty set]. It follows that X([0; 1]) is not homeomorphic to ...
    • 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 ...
    • 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. ...
    • 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 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.
    • 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 ...
    • 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.
    • Minimal Fine Derivatives and Brownian Excursions 

      Burdzy, Krzysztof (Nagoya University, 1990-09)
      Let f be an analytic function defined on D [is a subset of] [complex numbers] C. If [the derivative of the function f at the point x] has a limit when [the set] x [into the set] z [is an element of the set partial derivative] ...
    • No triple point of planar Brownian motion is accessible 

      Burdzy, Krzysztof; Werner, Wendelin (Institute of Mathematical Statistics, 1996-01)
      We show that the boundary of a connected component of the complement of a planar Brownian path on a fixed time-interval contains almost surely no triple point of this Brownian path.
    • Non-intersection exponents for Brownian paths. Part II: Estimations and applications to a random fractal. 

      Burdzy, Krzysztof; Lawler, Gregory F. (Institute of Mathematical Statistics, 1990-07)
      Let X and Y be independent two-dimensional Brownian motions, X(0) = (0; 0); Y(0) = ([epsilon]; 0), and let p([epsilon]) = P(X[0; 1] [intersected with] Y [0; 1] = [empty set], q([epsilon]) = {Y [0; 1] does not contain a ...
    • Non-polar points for reflected Brownian motion 

      Burdzy, Krzysztof; Marshall, Donald E. (Elsevier, 1993)
      Our main results are (i) a new construction of reflected Brownian motion X in a half-plane with non-smooth angle of oblique reflection and (ii) a theorem on existence of some "exceptional" points on the paths of the ...
    • On Brownian Excursions in Lipschitz Domains. Part II: Local Asymptotic Distributions 

      Burdzy, Krzysztof; Toby, Ellen H.; Williams, Ruth J. (Birkhäuser Boston, Inc., 1989)
      In this paper, we continue the study initiated in Burdzy and Williams (1986) of the local properties of Brownian excursions in Lipschitz domains. The focus in part I was on local path properties of such excursions. In ...