Pathwise Uniqueness of Non-uniformly Elliptic SDEs with Rough Coefficients

Olivier Menoukeu-Pamen; Youssef Ouknine; Ludovic Tangpi

doi:10.1007/s10959-018-0869-2

Pathwise Uniqueness of Non-uniformly Elliptic SDEs with Rough Coefficients

Olivier Menoukeu-Pamen, Youssef Ouknine, Ludovic Tangpi

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1892-1908
Number of pages	17
Journal	Journal of Theoretical Probability
Volume	32
Issue number	4
DOIs	https://doi.org/10.1007/s10959-018-0869-2
State	Published - Dec 1 2019
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistics and Probability
General Mathematics
Statistics, Probability and Uncertainty

Keywords

Comparison theorem for local times
Local time of the unknown
Pathwise uniqueness
Stochastic differential equations

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10.1007/s10959-018-0869-2

Cite this

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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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AU - Menoukeu-Pamen, Olivier

AU - Ouknine, Youssef

AU - Tangpi, Ludovic

PY - 2019/12/1

Y1 - 2019/12/1

N2 - 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.

AB - 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.

KW - Comparison theorem for local times

KW - Local time of the unknown

KW - Pathwise uniqueness

KW - Stochastic differential equations

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Pathwise Uniqueness of Non-uniformly Elliptic SDEs with Rough Coefficients

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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