Pathwise Uniqueness of Non-uniformly Elliptic SDEs with Rough Coefficients



Menoukeu Pamen, OO, Ouknine, Youssef and Tangpi, Ludovic
(2019) Pathwise Uniqueness of Non-uniformly Elliptic SDEs with Rough Coefficients. Journal of Theoretical Probability, 32 (4). 1892 - 1908.

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Abstract

In this paper, we review and improve pathwise uniqueness results for some types of one-dimensional stochastic differential equations (SDE) involving the local time of the unknown process. The diffusion coefficient of the SDEs we consider is allowed to vanish on a set of positive measure and is not assumed to be smooth. As opposed to various existing results, our arguments are mainly based on the comparison theorem for local time and the occupation time formula. We apply our pathwise uniqueness results to derive strong existence and other properties of solutions for SDEs with rough coefficients.

Item Type: Article
Uncontrolled Keywords: Stochastic differential equations, Pathwise uniqueness, Comparison theorem for local times, Local time of the unknown
Depositing User: Symplectic Admin
Date Deposited: 15 Nov 2018 09:20
Last Modified: 22 Jan 2021 12:35
DOI: 10.1007/s10959-018-0869-2
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3028865