Geodesic
On Infinite Systems of Linear Autonomous and Nonautonomous Stochastic Equations
Matematičeskie zametki, Tome 71 (2002) no. 6, pp. 890-901 
T. S. Rybnikova. On Infinite Systems of Linear Autonomous and Nonautonomous Stochastic Equations. Matematičeskie zametki, Tome 71 (2002) no. 6, pp. 890-901. http://geodesic.mathdoc.fr/item/MZM_2002_71_6_a8/
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     author = {T. S. Rybnikova},
     title = {On {Infinite} {Systems} of {Linear} {Autonomous} and {Nonautonomous} {Stochastic} {Equations}},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_71_6_a8/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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