On existence, and stability of solutions of stochastic integral equations (Q1390150)

A theorem is proved establishing the existence and asymptotic behavior of a solution of a nonlinear stochastic integral equation of the form \[ X (t;\omega) =h\bigl( t,X(t; \omega) \bigr)+ \int^t_0 f\bigl(t,s,X (s;\omega); \omega \bigr)ds+ \int^t_0 g\bigl(t,s,X (s;\omega); \omega\bigr) d\beta (s;\omega) \] under weaker conditions than the standard ones. The authors note that a similar proof will establish the same type of results for the analogous stochastic functional integral equation.