Harnack Inequalities for Stochastic Partial Differential Equations
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.
Focuses on dimension-free Harnack inequalities with applications to typical models of stochastic partial/delayed differential equationsA useful reference for researchers and graduated students in probability theory, stochastic analysis, partial differential equations and functional analysis Comparing with exiting Harnack inequalities in analysis which applies only to finite-dimensional models, those introduced in the book are dimension-free and thus are efficient also in infinite dimensions