Asymptotic behavior of solutions of linear stochastic differential systems

Friedman, Avner; Pinsky, Mark A.

doi:10.1090/S0002-9947-1973-0319268-3

Asymptotic behavior of solutions of linear stochastic differential systems
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by Avner Friedman and Mark A. Pinsky PDF

Trans. Amer. Math. Soc. 181 (1973), 1-22 Request permission

Abstract:

Following Kasminski, we investigate asymptotic behavior of solutions of linear time-independent Itô equations. We first give a sufficient condition for asymptotic stability of the zero solution. Then in dimension 2 we determine conditions for spiraling at a linear rate. Finally we give applications to the Cauchy problem for the associated parabolic equation by the use of a tauberian theorem.

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