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

Zhen Wang; Xicheng Zhang

doi:10.1016/j.jmaa.2019.123679

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

Zhen Wang^*, Xicheng Zhang

^*Corresponding author for this work

Wuhan University

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

1 Citation (Scopus)

Abstract

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.

Original language	English
Article number	123679
Journal	Journal of Mathematical Analysis and Applications
Volume	484
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2019.123679
Publication status	Published - 1 Apr 2020
Externally published	Yes

Keywords

Krylov's estimate
Multidimensional SDE
Pathwise uniqueness

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10.1016/j.jmaa.2019.123679

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title = "Existence and uniqueness of degenerate SDEs with H{\"o}lder diffusion and measurable drift",

abstract = "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 H{\"o}lder diffusion coefficients are provided to show our results.",

keywords = "Krylov's estimate, Multidimensional SDE, Pathwise uniqueness",

author = "Zhen Wang and Xicheng Zhang",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

year = "2020",

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T1 - Existence and uniqueness of degenerate SDEs with Hölder diffusion and measurable drift

AU - Wang, Zhen

AU - Zhang, Xicheng

PY - 2020/4/1

Y1 - 2020/4/1

N2 - 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.

AB - 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.

KW - Krylov's estimate

KW - Multidimensional SDE

KW - Pathwise uniqueness

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U2 - 10.1016/j.jmaa.2019.123679

DO - 10.1016/j.jmaa.2019.123679

M3 - Article

AN - SCOPUS:85075967726

SN - 0022-247X

VL - 484

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

M1 - 123679

ER -

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

Abstract

Keywords

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