TY - JOUR
T1 - Pathwise Uniqueness of Non-uniformly Elliptic SDEs with Rough Coefficients
AU - Menoukeu-Pamen, Olivier
AU - Ouknine, Youssef
AU - Tangpi, Ludovic
N1 - Funding Information:
Financial support from the Alexander von Humboldt Foundation under the programme financed by the German Federal Ministry of Education and Research entitled German Research Chair No. 01DG15010 is gratefully acknowledged.
Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.
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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U2 - 10.1007/s10959-018-0869-2
DO - 10.1007/s10959-018-0869-2
M3 - Article
AN - SCOPUS:85057337478
SN - 0894-9840
VL - 32
SP - 1892
EP - 1908
JO - Journal of Theoretical Probability
JF - Journal of Theoretical Probability
IS - 4
ER -