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#### Local time flow related to skew Brownian motion

(Institute of Mathematical Statistics, 2001-10)

We define a local time flow of skew Brownian motions, i.e., a family of solutions to the stochastic differential equation defining the skew Brownian motion, starting from different points but driven by the same Brownian motion. We prove several results on distributional and path properties of the flow. Our main result is a ...

#### Variably skewed Brownian motion

(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 ...

#### The supremum of Brownian local times on Holder curves

(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 ...

#### Uniqueness for reflecting Brownian motion in lip domains

(Elsevier, 2005-03)

A lip domain is a Lipschitz domain where the Lipschitz constant is strictly less than one. We prove strong existence and pathwise uniqueness for the solution X = {X [subscript] t, t [is less than or equal to] 0} to the Skorokhod equation dX [subscript] t = dW [subscript] t + n(X [subscript] t)dL [subscript] t, in planar lip ...