Derivative formula and applications for degenerate diffusion semigroups

Feng Yu Wang; Xi Cheng Zhang

doi:10.1016/j.matpur.2012.10.007

Derivative formula and applications for degenerate diffusion semigroups

Feng Yu Wang^*, Xi Cheng Zhang

^*Corresponding author for this work

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

32 Citations (Scopus)

Abstract

By using the Malliavin calculus and solving a control problem, Bismut type derivative formulae are established for a class of degenerate diffusion semigroups with non-linear drifts. As applications, explicit gradient estimates and Harnack inequalities are derived.

Original language	English
Pages (from-to)	726-740
Number of pages	15
Journal	Journal des Mathematiques Pures et Appliquees
Volume	99
Issue number	6
DOIs	https://doi.org/10.1016/j.matpur.2012.10.007
Publication status	Published - Jun 2013
Externally published	Yes

Keywords

Derivative formula
Gradient estimate
Harnack inequality
Stochastic differential equation

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10.1016/j.matpur.2012.10.007

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title = "Derivative formula and applications for degenerate diffusion semigroups",

abstract = "By using the Malliavin calculus and solving a control problem, Bismut type derivative formulae are established for a class of degenerate diffusion semigroups with non-linear drifts. As applications, explicit gradient estimates and Harnack inequalities are derived.",

keywords = "Derivative formula, Gradient estimate, Harnack inequality, Stochastic differential equation",

author = "Wang, {Feng Yu} and Zhang, {Xi Cheng}",

year = "2013",

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AU - Zhang, Xi Cheng

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AB - By using the Malliavin calculus and solving a control problem, Bismut type derivative formulae are established for a class of degenerate diffusion semigroups with non-linear drifts. As applications, explicit gradient estimates and Harnack inequalities are derived.

KW - Derivative formula

KW - Gradient estimate

KW - Harnack inequality

KW - Stochastic differential equation

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U2 - 10.1016/j.matpur.2012.10.007

DO - 10.1016/j.matpur.2012.10.007

M3 - Article

AN - SCOPUS:84878130743

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JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

IS - 6

ER -

Derivative formula and applications for degenerate diffusion semigroups

Abstract

Keywords

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