Existence and uniqueness of the strong solution for a stochastic integral equation of Ito-Volterra type. (Russian) Zbl 0696.60059

Pikovskij, I. E.

Teor. Veroyatn. Mat. Stat., Kiev 41, 96-101 (1989).

The stochastic integral equation of Volterra type with anticipating kernels of the form \[ X(t)=X_ 0+\int^{t}_{0}K_ 1(t,s,X(s))dw_ s+\int^{t}_{0}K_ 2(t,s,X(s))ds \] is considered. Sufficient conditions for existence and uniqueness of the strong solution were found in the case of anticipating kernels with special representation of the form \[ K_ 1(t,s,x,\omega)=\sum^{\infty}_{i=0}a_ i(t,\omega)b_ i(s,x,\omega). \]

Reviewer: I.Pikovskij

MSC:

60H20

Stochastic integral equations

Keywords:

stochastic integral equation; anticipating kernels; existence and uniqueness of the strong solution