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2015 On countably skewed Brownian motion with accumulation point
Gerald Trutnau, Youssef Ouknine, Francesco Russo
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Electron. J. Probab. 20: 1-27 (2015). DOI: 10.1214/EJP.v20-3640

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.

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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

Information

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

zbMATH: 1327.31023
MathSciNet: MR3383566
Digital Object Identifier: 10.1214/EJP.v20-3640

Subjects:
Primary: 31C25 , 60J55 , 60J60
Secondary: 31C15 , 60B10

Keywords: Local time , Pathwise uniqueness , positive recurrence , recurrence , skew Brownian motion , strong existence , transience

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