Electronic Journal of Probability

On countably skewed Brownian motion with accumulation point

Gerald Trutnau, Youssef Ouknine, and Francesco Russo

Full-text: Open access

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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465067189

Digital Object Identifier
doi:10.1214/EJP.v20-3640

Mathematical Reviews number (MathSciNet)
MR3383566

Zentralblatt MATH identifier
1327.31023

Subjects
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

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

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

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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