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Preprints, Working Papers, ... Year : 2013

On countably skewed Brownian motion with accumulation point.

Youssef Ouknine
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Gerald Trutnau
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Abstract

In this work we connect the theory of Dirichlet forms and direct stochastic calculus to obtain strong existence and pathwise uniqueness for Brownian motion that is perturbed by a series of constant multiples of local times at a sequence of points that has exactly one accumulation point in $\mathbb{R}$. The considered process is identified as special distorted Brownian motion $X$ in dimension one and is studied thoroughly. Besides strong uniqueness, we present necessary and sufficient conditions for non-explosion, recurrence and positive recurrence as well as for $X$ to be semimartingale and possible applications to advection-diffusion in layered media.
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Dates and versions

hal-00850095 , version 1 (02-08-2013)

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  • HAL Id : hal-00850095 , version 1

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Youssef Ouknine, Francesco Russo, Gerald Trutnau. On countably skewed Brownian motion with accumulation point.. 2013. ⟨hal-00850095⟩
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