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    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 [beta] [subscript] a is carried by a set which has Hausdorff dimension equal to 2−a. A Palm measure ...
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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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    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 along the x-axis. The drift of the Brownian particle is induced by conditioning and by the asymmetry of the ...
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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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    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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    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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    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 function of time and its quadratic variation may be identified with a Brownian motion.
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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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    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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    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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    Burdzy, Krzysztof (21)
    Bass, Richard F. (7)Holyst, Robert (2)Salisbury, Thomas S. (2)Adelman, Omer (1)Banuelos, Rodrigo (1)Barlow, Martin T. (1)Frankel, David M. (1)Ingerman, David (1)Khoshnevisan, Davar (1)... View MoreSubject
    Brownian motion (21)
    local time (3)bifurcation time (2)diffusion (2)fractal (2)Martin boundary (2)4-stable process (1)arcsine law (1)asymptotic value (1)bifurcation (1)... View MoreDate Issued1999 (2)1998 (2)1997 (1)1996 (3)1995 (4)1994 (2)1993 (1)1992 (1)1990 (5)

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