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On Infinite Systems of Linear Autonomous and Nonautonomous Stochastic Equations
T. S. Rybnikova M. V. Lomonosov Moscow State University
Abstract:
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.
Received: 21.11.2001
Citation:
T. S. Rybnikova, “On Infinite Systems of Linear Autonomous and Nonautonomous Stochastic Equations”, Mat. Zametki, 71:6 (2002), 890–901; Math. Notes, 71:6 (2002), 815–824
Linking options:
https://www.mathnet.ru/eng/mzm393https://doi.org/10.4213/mzm393 https://www.mathnet.ru/eng/mzm/v71/i6/p890
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Abstract page: | 304 | Full-text PDF : | 101 | References: | 50 | First page: | 1 |
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