Integration by parts formulas and rotationally invariant Sobolev calculus on free loop spaces
The aim of this paper is to examine the Sobolev calculus on the path space and on the free loop space. In both cases the key theorem is the integration by parts formula. The Sobolev spaces and space of smooth functions are defined. Examples of such functions are given. One of them is the solution of the Stratonovich stochastic differential equation in \(R^ d\). An Ornstein-Uhlenbeck operator is also considered.
Stratonovich stochastic differential equation
scientific article; zbMATH DE number 436593