Now showing items 21-40 of 112

    • 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.
    • The Martin boundary in non-Lipschitz domains 

      Burdzy, Krzysztof; Bass, Richard F. (American Mathematical Society, 1993)
      The Martin boundary with respect to the Laplacian and with respect to uniformly elliptic operators in divergence form can be identified with the Euclidean boundary in C [to the power of gamma] domains, where [gamma](x) = ...
    • 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 domain monotonicity of the Neumann heat kernel 

      Burdzy, Krzysztof; Bass, Richard F. (Academic Press (Elsevier), 1993-08-15)
      Some examples are given of convex domains for which domain monotonicity of the Neumann heat kernel does not hold.
    • The boundary Harnack principle for non-divergence form elliptic operators 

      Burdzy, Krzysztof; Bass, Richard F. (Cambridge University Press, 1994)
      If L is a uniformly elliptic operator in non–divergence form, the boundary Harnack principle for the ratio of positive L–harmonic functions holds in Hölder domains of order [alpha] if [alpha] > 1/2. A counterexample shows ...
    • 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 ...
    • 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. ...
    • 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 ...
    • 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.
    • 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 ...
    • 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.
    • 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 ...
    • Conditioned Brownian motion in planar domains 

      Burdzy, Krzysztof; Bass, Richard F. (Springer-Verlag GmbH, 1995-04)
      We give an upper bound for the Green functions of conditioned Brownian motion in planar domains. A corollary is the conditional gauge theorem in bounded planar domains.
    • 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 ...
    • 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.
    • 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 ...
    • 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 ...
    • 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.
    • Configurational transition in a Fleming-Viot-type model and probabilistic interpretation of Laplacian eigenfunctions 

      Burdzy, Krzysztof; Holyst, Robert; Ingerman, David; March, Peter (Institute of Physics, 1996-06-07)
      We analyze and simulate a two-dimensional Brownian multi-type particle system with death and branching (birth) depending on the position of particles of different types. The system is confined in the two-dimensional box, ...
    • Isogonal prismatoids 

      Grünbaum, Branko (Springer New York, 1997)
      A prismatoid is a polyhedron with all vertices in two parallel planes. A polyhedron P is isogonal if all its vertices form one transitivity class under isometric symmetries of P. Although these restrictions appear very ...