On Infinite Systems of Linear Autonomous and Nonautonomous Stochastic Equations

The solvability of autonomous and nonautonomous stochastic linear differential equations in $\mathbb R^\infty$ is studied. The existence of strong continuous ($L^p$-continuous) solutions of autonomous linear stochastic differential equations in $\mathbb R^\infty$ with continuous ($L^p$-continuous) right-hand sides is proved. Uniqueness conditions are obtained. We give examples showing that both deterministic and stochastic linear nonautonomous differential equations with the same operator in $\mathbb R^\infty$ may fail to have a solution. We also establish existence and uniqueness conditions for nonautonomous equations.