Two-parameter stochastic calculus and Malliavin's integration-by-parts formula on Wiener space

2009/03/23 by James R. Norris, Norris, J. R.
Computer Science · Economics, Econometrics and Finance · Mathematics · #Algebraic and Geometric Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.0903.3855

openalex publication_date 2009/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The integration-by-parts formula discovered by Malliavin for the Ito map on Wiener space is proved using the two-parameter stochastic calculus. It is also shown that the solution of a one-parameter stochastic differential equation driven by a two-parameter semimartingale is itself a two-parameter semimartingale.

Related

• Analysis on Wiener Space and Applications
• Integration-by-Parts Characterizations of Gaussian Processes
• Stochastic manifolds
• Introduction to White Noise, Hida-Malliavin Calculus and Applications
• Malliavin Calculus and Stochastic Differential Equations