## On countably skewed Brownian motion with accumulation point.(English)Zbl 1327.31023

Summary: 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.

### MSC:

 31C25 Dirichlet forms 60J65 Brownian motion

### Keywords:

Dirichlet form; Brownian motion
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