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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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    Variably skewed Brownian motion 

    Burdzy, Krzysztof; Barlow, Martin T.; Kaspi, Haya; Mandelbaum, Avi (Institute of Mathematical Statistics, 2000-03-01)
    Given a standard Brownian motion B, we show that the equation X [subscript] t = x [subscript] 0 + B [subscript] t + [beta](L [to the power of X] [subscript] t ); t [is greater than or equal to] 0 ; has a unique strong solution X. Here L [to the power of X] is the symmetric local time of X at 0, and [beta] is a given differentiable ...
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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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    The supremum of Brownian local times on Holder curves 

    Burdzy, Krzysztof; Bass, Richard F. (Elsevier, 2001-11)
    For f : [maps the set] [0, 1] [into the set of real numbers] R, we consider L ([to the power of] f [subscript] t), the local time of spacetime Brownian motion on the curve f. Let S [subscript alpha] be the class of all functions whose Holder norm of order [alpha] is less than or equal to 1. We show that the supremum of L ...
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    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 time spent by Brownian motion on the curve [theta subscript epsilon] (s) before time t. If [epsilon] > 0 ...

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    Author
    Burdzy, Krzysztof (5)
    Bass, Richard F. (3)Barlow, Martin T. (1)Kaspi, Haya (1)Khoshnevisan, Davar (1)Mandelbaum, Avi (1)San Martin, Jaime (1)Subject
    Brownian motion (5)
    local time (5)
    bifurcation (1)bifurcation time (1)differential equations (1)excursions (1)exit system (1)fractional Brownian motion (1)Holder norm (1)intersection local time (1)... View MoreDate Issued2001 (1)2000 (1)1999 (1)1995 (1)1994 (1)

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