Successive approximations for solutions of stochastic integral equations of Volterra type (Q1079875)

The following Volterra stochastic equation \[ x(t)=\phi (t)\quad \sigma - r\leq t\leq \sigma \] \[ x(t)=\phi (t)+K_ 1(t)+\int^{t}_{\sigma}K_ 2(s,x_ s)dw(s)+\int^{t}_{\sigma}K_ 3(t,s,x_ s)ds\quad t\geq \sigma \] is considered in an abstract Wiener space (i,H,B), where w is a B-valued Wiener process. Under Caratheodory's conditions on the kernels \(K_ 2\), \(K_ 3\), the convergence in maximal quadratic mean of Picard's successive approximations to a solution of the above equation is proved.