Existence and uniqueness of degenerate SDEs with Hölder diffusion and measurable drift

Existence and uniqueness of degenerate SDEs with Hölder diffusion and measurable drift

In this paper we prove a new strong uniqueness result and a weak existence result for possibly degenerate multidimensional stochastic differential equations with Sobolev diffusion coefficients and rough drifts. In particular, examples with Hölder diffusion coefficients are provided to show our resul...

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Veröffentlicht in:Journal of mathematical analysis and applications 2020-04, Vol.484 (1), p.123679, Article 123679
Hauptverfasser: Wang, Zhen, Zhang, Xicheng
Format: Artikel
Sprache:eng
Schlagworte:
Krylov's estimate
Multidimensional SDE
Pathwise uniqueness
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Zusammenfassung:In this paper we prove a new strong uniqueness result and a weak existence result for possibly degenerate multidimensional stochastic differential equations with Sobolev diffusion coefficients and rough drifts. In particular, examples with Hölder diffusion coefficients are provided to show our results.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2019.123679