A stability theorem for stochastic differential equations with application to storage processes, random walks and optimal stochastic control problems

Abstract

For a sequence of stochastic differential equations of type X n(t)=X n(0)+ʃ t 0a N(S, X N(S−)) dA n(S)+ʃ t 0ʃ R\\{0}c n(S,X n(S−))d n(S,X n(S−),x) N ̃ n(ds dx)+B n(t) , a stability theorem is presented under an appropriate convergence mode of coefficients a n , c n , d n , driving processes A n , B n and martingale measures Ñ n . Applications to limit theorems for storage processes, random walks and optimal control problems are shown.