Electronic Journal of Probability

On countably skewed Brownian motion with accumulation point

Gerald Trutnau, Youssef Ouknine, and Francesco Russo

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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.

Article information

Electron. J. Probab., Volume 20 (2015), paper no. 82, 27 pp.

Accepted: 7 August 2015
First available in Project Euclid: 4 June 2016

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Zentralblatt MATH identifier

Primary: 31C25: Dirichlet spaces 60J60: Diffusion processes [See also 58J65] 60J55: Local time and additive functionals
Secondary: 31C15: Potentials and capacities 60B10: Convergence of probability measures

Skew Brownian motion local time strong existence pathwise uniqueness transience recurrence positive recurrence

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Trutnau, Gerald; Ouknine, Youssef; Russo, Francesco. On countably skewed Brownian motion with accumulation point. Electron. J. Probab. 20 (2015), paper no. 82, 27 pp. doi:10.1214/EJP.v20-3640. https://projecteuclid.org/euclid.ejp/1465067189

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