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Transactions of the American Mathematical Society

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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: 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\vert\xi (t) - \bar \sigma w(t){\vert^2} = O({t^{1 - \delta }})$ are derived, and various applications are given.


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Additional Information

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