Bismut Formulae and Applications for Functional SPDEs
Jianhai Bao, Feng-Yu Wang, Chenggui Yuan
TL;DR
This paper develops Bismut formulae for functional SPDEs using Malliavin calculus, enabling gradient estimates and Harnack inequalities for the associated semigroup, advancing the analysis of stochastic partial differential equations.
Contribution
It introduces explicit derivative formulae for a class of functional SPDEs, expanding the toolkit for analyzing their properties using Malliavin calculus.
Findings
Derived gradient estimates for the semigroup
Established Harnack inequalities for the segment process
Provided explicit Bismut formulae for functional SPDEs
Abstract
By using Malliavin calculus, explicit derivative formulae are established for a class of semi-linear functional stochastic partial differential equations with additive or multiplicative noise. As applications, gradient estimates and Harnack inequalities are derived for the semigroup of the associated segment process. Keywords: Bismut formula, Malliavin calculus, gradient estimate, Harnack inequality, functional SPDE
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Taxonomy
TopicsStochastic processes and financial applications · Point processes and geometric inequalities · Geometric Analysis and Curvature Flows