On countably skewed Brownian motion with accumulation point.

Youssef Ouknine, Francesco Russo and Gerald Trutnau
august, 2015
Publication type:
Paper in peer-reviewed journals
Journal:
Electronic Journal in Probability., vol. 20 (82), pp. 1-27
arXiv:
images/icons/icon_arxiv.png 1308.0441
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},
}