Stochastic differential equations of jump type on manifolds and Lévy flows

Abstract

In the previous paper Fujiwara-Kunita [3], we have clarified the structure of C (le, le)-L vy flow s, i.e., stochastic processes w ith v a lu e s in th e semigroup C(R d , R d ) o f c o n tin u o u s m a p p in g s o n le w ith s ta tio n a r y in d e p e n d e n t increm ents. M o re concretely, w e constructed those stochastic flow s by som e stochastic differential equations of jum p type, and conversely when the stochastic flow was given, we represented it as the system of solutions of the same type of stochastic differential equation. I n t h i s w a y , w e e sta b lish e d a one-to-one correspondence between a general class o f C(le, 1V)-Lvy flows a n d a class of stochastic differential equations which govern the flows.