Stochastic Volterra equations driven by cylindrical Wiener process. (English) Zbl 1120.60062

Karczewska, Anna; Lizama, Carlos

J. Evol. Equ. 7, No. 2, 373-386 (2007).

Summary: Stochastic Volterra equations driven by cylindrical Wiener process in Hilbert space are investigated. Sufficient conditions for the existence of strong solutions are given. The key role is played by convergence of \(\alpha\)-times resolvent families.

MSC:

60H20	Stochastic integral equations
60H05	Stochastic integrals
45D05	Volterra integral equations

Keywords:

stochastic Volterra equation; \(\alpha\)-times resolvent family; strong solution; stochastic convolution; convergence of resolvent families