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# On countably skewed Brownian motion with accumulation point.

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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https://hal.inria.fr/hal-00850095
Contributor : Francesco Russo Connect in order to contact the contributor
Submitted on : Friday, August 2, 2013 - 4:04:23 PM
Last modification on : Monday, November 30, 2020 - 3:38:06 PM
Long-term archiving on: : Sunday, November 3, 2013 - 1:11:31 PM

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ORTMultiskewAugust2013Sent.pdf
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• HAL Id : hal-00850095, version 1

### Citation

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

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