Abstract
In this work we connect the theory of symmetric 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.
Citation
Gerald Trutnau. Youssef Ouknine. Francesco Russo. "On countably skewed Brownian motion with accumulation point." Electron. J. Probab. 20 1 - 27, 2015. https://doi.org/10.1214/EJP.v20-3640
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