Malliavin calculus and stochastic differential equations
Abstract
This paper is devoted to a study on SDEs with a bounded Borel drift $ b $. First, we remark that the original integration by parts formula due to P. Malliavin [14] can be used to deal with derivatives with respect to space variables. Then we obtain a link between the product of heat kernels and iterated divergences in Malliavin calculus. An explicit estimate for the derivative of solutions to SDE is obtained in terms of $ ||b||_\infty $. As a result, we prove that the SDE defines a continuous flow of maps in Sobolev spaces.
Fields of Study & Subjects
Stochastic processes and financial applications
Geometric Analysis and Curvature Flows
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- Communications on Pure & Applied Analysis
- Volume
- 32
- Issue
- 0
- Pages
- 171–191
- Publication date
- 1 January 2026
- Language
- EN