Existence of solutions of general nonlinear stochastic integral equations (Q1366937)

Under assumptions more general than previously employed in the literature, this paper provides a proof of the existence of a solution \(x(t;\omega)\) of the nonlinear stochastic integral equation \[ x(t;\omega)=h(t,x(t;\omega))+ \sum^m_{i=1}\int^t_0 a_i(t,\tau;\omega)f_i(\tau, x(\tau,\omega))d\tau+ \sum^n_{j=1} \int^t_0 b_j(t,\tau;\omega)g_j(\tau, x(\tau;\omega))d\beta(\tau;\omega). \]