Limit of Solutions of a SDE with a Large Drift Driven by a Poisson Random Measure

We consider a sequence of {X_n} of R^d-valued processes satisfying a stochastic differential equation driven by a Brownian motion and a compensated Poisson random measure, with _n~_n with a large drift. Let be a m-dimensional submanifold (m<d), where F vanishes. Then under some suitable growth conditions for _n~_n, and some conditions for F, we show that dist(X_n, )0 before it exits any given compact set, that is, the large drift term forces X_n close to . And if the coefficients converge to some continuous functions, any limit process must actually stay on and satisfy a certain stochastic differential equation driven by Brownian motion and white noise.