On countably skewed Brownian motion with accumulation point.
august, 2015
Publication type:
Paper in peer-reviewed journals
Journal:
Electronic Journal in Probability., vol. 20 (82), pp. 1-27
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Keywords :
Skew Brownian motion; local time; strong existence; pathwise uniqueness; transience; recurrence; positive recurrence.
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.
BibTeX:
@article{Ouk-Rus-Tru-2015, author={Youssef Ouknine and Francesco Russo and Gerald Trutnau }, title={On countably skewed Brownian motion with accumulation point. }, doi={10.1214/EJP.v20-3640 }, journal={Electronic Journal in Probability. }, year={2015 }, month={8}, volume={20 (82) }, pages={1--27}, }