Limit behavior of solutions of stochastic differential equations

Friedman, Avner

doi:10.1090/S0002-9947-1972-0378118-9

Limit behavior of solutions of stochastic differential equations
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by Avner Friedman

Trans. Amer. Math. Soc. 170 (1972), 359-384

DOI: https://doi.org/10.1090/S0002-9947-1972-0378118-9

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Abstract:

Consider a system of $m$ stochastic differential equations $d\xi = a(t,\xi )dt + \sigma (t,\xi )dw$. The limit behavior of $\xi (t)$, as $t \to \infty$, is studied. Estimates of the form $E|\xi (t) - \bar \sigma w(t){|^2} = O({t^{1 - \delta }})$ are derived, and various applications are given.

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