×

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
PDF BibTeX XML Cite
Full Text: DOI arXiv