Bismut Formulae and Applications for Functional SPDEs

2011/10/24 by Jianhai Bao, Bao, Jianhai, Feng‐Yu Wang +3
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1110.5150

openalex publication_date 2011/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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

Citations

• Degenerate Fokker-Planck Equations : Bismut Formula, Gradient Estimate and Harnack Inequality
• Derivative Formula and Applications for Degenerate Diffusion Semigroups

Related

• Bismut formulae and applications for stochastic (functional) differential equations driven by fractional Brownian motions
• The Bismut-Elworthy-Li formula for mean-field stochastic differential\n equations
• Bismut Formula and Gradient Estimates for Dirichlet Semigroups with Application to Singular Killed DDSDEs
• Gradient estimates for SDEs Driven by Multiplicative Lévy Noise
• Integration by Parts Formula and Applications for SDEs with Lévy Noise