On the existence and uniqueness of a solution of a stochastic differential equations with martingale differential
Abstract
Under some conditions, the existence and uniqueness of a solution of the equation $$ d\xi(t)=a(t,\xi(t))dt+\sum_{k=1}^rb_k(t,\xi(t))d\zeta_k(t)+\int_{R^m}f(t,\xi(t),u)\widetilde\nu(dt,du) $$are proved, where$\zeta_k(t)$,$k=\overline{1,r}$, are continuous martingales,$\widetilde\nu(t,A)=\nu(t,A)-t\Pi(A)$and$\nu(t,A)$is a Poisson measure,$\mathbf M\nu(t,A)=t\Pi(A)$.
Submission history
[v1] 1974