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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


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.


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

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

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


Vol.20 • 2015
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