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    Percolation dimension of fractals 

    Burdzy, Krzysztof (Academic Press (Elsevier), 1990-01)
    "Percolation dimension" is introduced in this note. It characterizes certain fractals and its definition is based on the Hausdorff dimension. It is shown that percolation dimension and "boundary dimension" are in a sense independent from the Hausdorff dimension and, therefore, provide an additional tool for classification of ...
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    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.
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    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 standard two-dimensional Brownian motion. The link between these two seemingly disparate results will be formed ...
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    Sets avoided by Brownian motion 

    Burdzy, Krzysztof; Adelman, Omer; Pemantle, Robin (Institute of Mathematical Statistics, 1998-04)
    A fixed two-dimensional projection of a three-dimensional Brownian motion is almost surely neighborhood recurrent; is this simultaneously true of all the two-dimensional projections with probability one? Equivalently: three-dimensional Brownian motion hits any infinite cylinder with probability one; does it hit all cylinders? ...
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    On minimal parabolic functions and time-homogenous parabolic h-transforms 

    Burdzy, Krzysztof; Salisbury, Thomas S. (American Mathematical Society, 1999-03-29)
    Does a minimal harmonic function h remain minimal when it is viewed as a parabolic function? The question is answered for a class of long thin semi-infinite tubes D [is an element of the subset of real numbers to the power of] d of variable width and minimal harmonic functions h corresponding to the boundary point of D "at ...
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    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 closed loop around 0}. Asymptotic estimates (when [epsilon] --> 0) of p([epsilon]); q([epsilon]), and some ...
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    A representation of local time for Lipschitz surfaces 

    Banuelos, Rodrigo; Bass, Richard F.; Burdzy, Krzysztof (Springer-Verlag GmbH, 1990)
    Suppose that D [is an element of the set of Real numbers to the power of n], n [is greater than or equal to] 2, is a Lipschitz domain and let N[subscript]t(r) be the number of excursions of Brownian motion inside D with diameter greater than r which started before time t. Then rN[subscript]t(r) converges as r --> 0 to a ...
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    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.
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    Stochastic bifurcation models 

    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 direction of bifurcation. A relationship with Lipschitz approximations to Brownian paths is also discussed.
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    Weak convergence of reflecting Brownian motions 

    Burdzy, Krzysztof; Chen, Zhen-Qing (Institute of Mathematical Statistics, 1998-05-23)
    We will show that if a sequence of domains D [subscript] k increases to a domain D then the reflected Brownian motions in D [subscript] k's converge to the reflected Brownian motion in D, under mild technical assumptions. Our theorem follows easily from known results and is perhaps known as a "folk law" among the specialists ...
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    Burdzy, Krzysztof (44)
    Bass, Richard F. (15)Holyst, Robert (4)Banuelos, Rodrigo (3)Khoshnevisan, Davar (3)Ingerman, David (2)Lawler, Gregory F. (2)Madrecki, Andrzej (2)Marshall, Donald E. (2)Salisbury, Thomas S. (2)... View MoreSubjectBrownian motion (21)boundary Harnack principle (4)conditioned Brownian motion (4)Hölder domains (4)iterated Brownian motion (4)diffusion (3)eigenvalues (3)harmonic functions (3)Hausdorff dimension (3)local time (3)... View MoreDate Issued1999 (6)1998 (4)1997 (1)1996 (5)1995 (6)1994 (4)1993 (6)1992 (3)1991 (2)1990 (7)

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