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    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 the Sierpinski carpet a.s.
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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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    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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    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. For large N, the particle distribution density converges to the normalized heat equation solution in D ...
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    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 path. We show that there exist two different natural local times for a Brownian path reflected on a Brownian path.
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    On non-increase of Brownian motion 

    Burdzy, Krzysztof (Institute of Mathematical Statistics, 1990-07)
    A new proof of the non-increase of Brownian paths is given.
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    Burdzy, Krzysztof (32)
    Bass, Richard F. (10)Holyst, Robert (3)Barlow, Martin T. (2)Chen, Zhen-Qing (2)Salisbury, Thomas S. (2)San Martin, Jaime (2)Toby, Ellen H. (2)Adelman, Omer (1)Banuelos, Rodrigo (1)... View MoreSubject
    Brownian motion (32)
    local time (5)fractal (3)bifurcation time (2)Brownian excursions (2)Brownian paths (2)diffusion (2)Heat equation (2)Martin boundary (2)4-stable process (1)... View MoreDate Issued2000 - 2005 (7)1990 - 1999 (21)1989 - 1989 (4)

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