On a class of stochastic integro-differential equations

ABSTRACT

We prove the existence and uniqueness of a bounded random solution for a nonlinear stochastic integrodifferential equation on ${\mathbb{R}}_{+}$. We also show that the sequence of successive approximations converges to the solution $x(t,\omega )$ almost surely and in mean square at each $t\in {\mathbb{R}}_{+}$. An application of our result to a stochastic differential system is also given in Section 4.

Keywords:

• Stochastic integral equations
• applications of stochastic analysis
• stochastic differential system
• almost sure and mean square convergence

AMS Classifications:

• 60H20
• 60H30

Disclosure statement

No potential conflict of interest was reported by the author(s).