INTEGRATION BY PARTS FORMULA AND SHIFT HARNACK INEQUALITY FOR STOCHASTIC EQUATIONS
成果类型：
Article
署名作者：
Wang, Feng-Yu
署名单位：
Beijing Normal University; Swansea University
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/13-AOP875
发表日期：
2014
页码：
994-1019
关键词：
摘要：
A new coupling argument is introduced to establish Driver's integration by parts formula and shift Harnack inequality. Unlike known coupling methods where two marginal processes with different starting points are constructed to move together as soon as possible, for the new-type coupling the two marginal processes start from the same point but their difference is aimed to reach a fixed quantity at a given time. Besides the integration by parts formula, the new coupling method is also efficient to imply the shift Harnack inequality. Differently from known Harnack inequalities where the values of a reference function at different points are compared, in the shift Harnack inequality the reference function, rather than the initial point, is shifted. A number of applications of the integration by parts and shift Harnack inequality are presented. The general results are illustrated by some concrete models including the stochastic Hamiltonian system where the associated diffusion process can be highly degenerate, delayed SDEs and semi-linear SPDEs.