Integration by Parts Formula on Solutions to Stochastic Differential Equations with Jumps on Riemannian Manifolds

Abstract

Consider solutions to Marcus-type stochastic differential equations with jumps on the bundle of orthonormal frames O(M) over a Riemannian manifold M , and define the M -valued process by its canonical projection, which is parallel to the Eells-Elworthy-Malliavin construction of Brownian motions on M . In the present paper, the integration by parts formula for such jump processes is studied, and the strategy is based upon the calculus on Brownian motions via the Kolmogorov backward equations. The celebrated Bismut formula can be also obtained in our setting.