Sobolev differentiable flows of SDEs with local Sobolev and super-linear growth coefficients

Longjie Xie; Xicheng Zhang

doi:10.1214/15-AOP1057

Sobolev differentiable flows of SDEs with local Sobolev and super-linear growth coefficients

Longjie Xie, Xicheng Zhang

Wuhan University

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

22 Citations (Scopus)

Abstract

By establishing a characterization for Sobolev differentiability of random fields, we prove the weak differentiability of solutions to stochastic differential equations with local Sobolev and super-linear growth coefficients with respect to the starting point. Moreover, we also study the strong Feller property and the irreducibility to the associated diffusion semigroup.

Original language	English
Pages (from-to)	3661-3687
Number of pages	27
Journal	Annals of Probability
Volume	44
Issue number	6
DOIs	https://doi.org/10.1214/15-AOP1057
Publication status	Published - 2016
Externally published	Yes

Keywords

Irreducibility
Krylov's estimate
Strong Feller property
Weak differentiability
Zvonkin's transformation

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10.1214/15-AOP1057

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abstract = "By establishing a characterization for Sobolev differentiability of random fields, we prove the weak differentiability of solutions to stochastic differential equations with local Sobolev and super-linear growth coefficients with respect to the starting point. Moreover, we also study the strong Feller property and the irreducibility to the associated diffusion semigroup.",

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AU - Xie, Longjie

AU - Zhang, Xicheng

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PY - 2016

Y1 - 2016

N2 - By establishing a characterization for Sobolev differentiability of random fields, we prove the weak differentiability of solutions to stochastic differential equations with local Sobolev and super-linear growth coefficients with respect to the starting point. Moreover, we also study the strong Feller property and the irreducibility to the associated diffusion semigroup.

AB - By establishing a characterization for Sobolev differentiability of random fields, we prove the weak differentiability of solutions to stochastic differential equations with local Sobolev and super-linear growth coefficients with respect to the starting point. Moreover, we also study the strong Feller property and the irreducibility to the associated diffusion semigroup.

KW - Irreducibility

KW - Krylov's estimate

KW - Strong Feller property

KW - Weak differentiability

KW - Zvonkin's transformation

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JO - Annals of Probability

JF - Annals of Probability

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ER -

Sobolev differentiable flows of SDEs with local Sobolev and super-linear growth coefficients

Abstract

Keywords

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