Bismut type differentiation of semigroups (Q2769656)

Let NEWLINE\[NEWLINE\delta X= A(X)\delta Z+ A_0(X) dt\tag{1}NEWLINE\]NEWLINE be a Stratonovich stochastic differential equation on smooth \(n\)-dimensional manifold. The authors consider the minimal semigroup to (1) on functions and forms and present the Bismut type differentiation formulas for this semigroup in the case elliptic and hypoelliptic. This result is extended to nonlinear situations, to the harmonic maps between Riemannian manifolds and to the solutions of nonlinear heat equation.NEWLINENEWLINEFor the entire collection see [Zbl 0968.00043].