Pathwise Uniqueness of Non-uniformly Elliptic SDEs with Rough Coefficients

Olivier Menoukeu-Pamen (), Youssef Ouknine () and Ludovic Tangpi ()
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Olivier Menoukeu-Pamen: African Institute for Mathematical Sciences
Youssef Ouknine: Mohammed VI Polytechnic University
Ludovic Tangpi: Princeton University

Journal of Theoretical Probability, 2019, vol. 32, issue 4, 1892-1908

Abstract: 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.

Keywords: Stochastic differential equations; Pathwise uniqueness; Comparison theorem for local times; Local time of the unknown; 60H10; 60H60; 60J55 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10959-018-0869-2

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