ResearchWorks Archive

Browsing EPrint Collection - Mathematics by Issue Date

Browsing EPrint Collection - Mathematics by Issue Date

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  • Burdzy, Krzysztof (Springer Science+Business Media B.V., 1993)
    Three-dimensional Brownian path reflected on Brownian path is a free Brownian path.
  • 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) = ...
  • 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.
  • 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.
  • 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 ...
  • 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 ...
  • 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. ...
  • 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 ...
  • 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.
  • 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 ...
  • 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.
  • 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 ...
  • 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.
  • 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 ...
  • 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 ...
  • 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.
  • 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 ...
  • Burdzy, Krzysztof; Madrecki, Andrzej (Institute of Mathematical Statistics, 1996-02)
    An Ito-type formula is given for an asymptotically 4-stable process.
  • 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, ...
  • Grünbaum, Branko (1997)

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