Harnack Inequalities for Stochastic Partial Differential Equations

Nonfiction, Science & Nature, Mathematics, Differential Equations, Statistics
Cover of the book Harnack Inequalities for Stochastic Partial Differential Equations by Feng-Yu Wang, Springer New York
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Author: Feng-Yu Wang ISBN: 9781461479345
Publisher: Springer New York Publication: August 13, 2013
Imprint: Springer Language: English
Author: Feng-Yu Wang
ISBN: 9781461479345
Publisher: Springer New York
Publication: August 13, 2013
Imprint: Springer
Language: English

​In this book the author presents a self-contained account of Harnack inequalities and applications for the semigroup of solutions to stochastic partial and delayed differential equations. Since the semigroup refers to Fokker-Planck equations on infinite-dimensional spaces, the Harnack inequalities the author investigates are dimension-free. This is an essentially different point from the above mentioned classical Harnack inequalities. Moreover, the main tool in the study is a new coupling method (called coupling by change of measures) rather than the usual maximum principle in the current literature.

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​In this book the author presents a self-contained account of Harnack inequalities and applications for the semigroup of solutions to stochastic partial and delayed differential equations. Since the semigroup refers to Fokker-Planck equations on infinite-dimensional spaces, the Harnack inequalities the author investigates are dimension-free. This is an essentially different point from the above mentioned classical Harnack inequalities. Moreover, the main tool in the study is a new coupling method (called coupling by change of measures) rather than the usual maximum principle in the current literature.

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