Pathwise uniqueness of non-uniformly elliptic SDEs with rough coefficients

Olivier Menoukeu-Pamen; Youssef Ouknine; Ludovic Tangpi

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arXiv · 1712.08237

Pathwise uniqueness of non-uniformly elliptic SDEs with rough coefficients

Olivier Menoukeu-Pamen·Youssef Ouknine·Ludovic Tangpi

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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.

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Olivier Menoukeu-Pamen, Youssef Ouknine, Ludovic Tangpi. 2017-12-21. Pathwise uniqueness of non-uniformly elliptic SDEs with rough coefficients. https://arxiv.org/abs/1712.08237

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