Yu. V. Mednitskii, “On the existence of strong solutions of linear stochastic differential equations in <nobr>$\mathbb{R}^\infty$</nobr>”, Teor. Veroyatnost. i Primenen., 1997, Volume 42, Issue 4,Pages <nobr>826

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Short Communications

On the existence of strong solutions of linear stochastic differential equations in $\mathbb{R}^\infty$

Yu. V. Mednitskii

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

Abstract: In this work we prove the existence of a strong solution of a linear stochastic differential equation in $\mathbb R^\infty$. We use an infinite-dimensional modification of the method of successive approximations to find a solution to systems of a special form as well as an analogue of the Jordan method of reducing a matrix to a block form. The nonuniqueness of the constructed solution is shown.

Received: 24.04.1996

DOI: 10.4213/tvp2615