Pathwise Uniqueness of Non-uniformly Elliptic SDEs with Rough Coefficients

Olivier Menoukeu-Pamen, Youssef Ouknine, Ludovic Tangpi Ndounkeu

Research output: Contribution to journalArticle

1 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 languageEnglish (US)
Pages (from-to)1892-1908
Number of pages17
JournalJournal of Theoretical Probability
Volume32
Issue number4
DOIs
StatePublished - Dec 1 2019

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

Keywords

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

Fingerprint Dive into the research topics of 'Pathwise Uniqueness of Non-uniformly Elliptic SDEs with Rough Coefficients'. Together they form a unique fingerprint.

  • Cite this