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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Asymptotic behavior of solutions of linear stochastic differential systems


Authors: Avner Friedman and Mark A. Pinsky
Journal: Trans. Amer. Math. Soc. 181 (1973), 1-22
MSC: Primary 60H10
DOI: https://doi.org/10.1090/S0002-9947-1973-0319268-3
MathSciNet review: 0319268
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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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DOI: https://doi.org/10.1090/S0002-9947-1973-0319268-3
Keywords: Stochastic differential equation, diffusion process, asymptotic stability, spiraling solutions
Article copyright: © Copyright 1973 American Mathematical Society