ISSN:
1572-9230
Keywords:
SDE
;
Poisson random measure
;
martingale measure
;
weak convergence
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract 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 ε n ~ν n with a large drift. Let Γ be a m-dimensional submanifold (m〈d), where F vanishes. Then under some suitable growth conditions for ε n ~ν n, and some conditions for F, we show that dist(X n, Γ)⇒0 before it exits any given compact set, that is, the large drift term forces X n close to Γ. And if the coefficients converge to some continuous functions, any limit process must actually stay on Γ and satisfy a certain stochastic differential equation driven by Brownian motion and white noise.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1007853810143
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