On the Existence, Uniqueness, Convergence and Explosions of Solutions of Systems of Stochastic Integral Equations

Abstract

A theory of stochastic integral equations is developed for the integrals of Kunita, Watanabe, and P. A. Meyer. Existence and uniqueness of solutions of systems of equations with semimartingale (or "quasi-martingale") differentials is proved, in which we include as particular cases the customary results as put forth by McKean and Gihman and Skorohod. Under weaker conditions we prove existence and uniqueness with explosions, and study the explosion times. We show that when the (random) coefficients or the differentials converge, the solutions converge to the solution of the limiting equation.