# On countably skewed Brownian motion with accumulation point.

Abstract : In this work we connect the theory of 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.
Keywords :
Type de document :
Pré-publication, Document de travail
2013
Domaine :

https://hal.inria.fr/hal-00850095
Contributeur : Francesco Russo <>
Soumis le : vendredi 2 août 2013 - 16:04:23
Dernière modification le : jeudi 16 novembre 2017 - 17:15:02
Document(s) archivé(s) le : dimanche 3 novembre 2013 - 13:11:31

### Fichiers

ORTMultiskewAugust2013Sent.pdf
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### Identifiants

• HAL Id : hal-00850095, version 1

### Citation

Youssef Ouknine, Francesco Russo, Gerald Trutnau. On countably skewed Brownian motion with accumulation point.. 2013. 〈hal-00850095〉

### Métriques

Consultations de la notice

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