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Short Communications

On linear row-finite systems of stochastic differential equations

T. S. Rybnikova

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We discuss the existence of solutions of linear stochastic differential equations in $\mathbf{R}^\infty$. The existence of strong continuous (respectively, $L^p$-continuous) solutions of autonomous linear stochastic differential equations in $\mathbf{R}^\infty$ with continuous (respectively, $L^p$-continuous) right-hand sides is proved. Uniqueness conditions are obtained.

Keywords: linear stochastic differential equation, strong solution, adapted process.

Received: 23.06.1999

DOI: 10.4213/tvp489

 English version: Theory of Probability and its Applications, 2001, 45:3, 539–545

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