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On Infinite Systems of Linear Autonomous and Nonautonomous Stochastic Equations

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Abstract

The solvability of autonomous and nonautonomous stochastic linear differential equations in ℝ∞ is studied. The existence of strong continuous (Lp-continuous) solutions of autonomous linear stochastic differential equations in ℝ∞ with continuous (Lp-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 ℝ∞ may fail to have a solution. We also establish existence and uniqueness conditions for nonautonomous equations.

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  1. M. V. Lomonosov Moscow State University, Russia

    T. S. Rybnikova

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  1. T. S. Rybnikova
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Rybnikova, T.S. On Infinite Systems of Linear Autonomous and Nonautonomous Stochastic Equations. Mathematical Notes 71, 815–824 (2002). https://doi.org/10.1023/A:1015825029763

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