Limit behavior of solutions of stochastic differential equations

Author:
Avner Friedman

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

MSC:
Primary 60J60

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

MathSciNet review:
0378118

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Abstract | References | Similar Articles | Additional Information

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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Keywords:
Limit behavior,
stochastic differential equations,
Brownian motion,
asymptotic behavior of solutions,
diffusion matrix,
exit time,
parabolic equations,
Ito formula,
convergence in distribution,
Cauchy problem

Article copyright:
© Copyright 1972
American Mathematical Society