Abstract Volterra equations with stochastic kernels. (English. Ukrainian original) Zbl 0998.60054

Mishura, Yu. S.

Theory Probab. Math. Stat. 64, 139-151 (2002); translation from Teor. Jmovirn. Mat. Stat. 64, 118-128 (2001).

The Volterra equation \[ x(t,\omega)=f(t,\omega)+\int_0^t a(t-s,\omega)Ax(s,\omega)ds \] with the stochastic kernel \(a(t,\omega)\) is considered. The author proposes a sufficient condition for existence and uniqueness of a solution to this equation. As application, an equation from fluid mechanics is investigated.

Reviewer: M.P.Moklyachuk (Kyïv)

MSC:

60H05	Stochastic integrals
76M35	Stochastic analysis applied to problems in fluid mechanics
60H07	Stochastic calculus of variations and the Malliavin calculus

Keywords:

Volterra equation; stochastic kernel