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Transactions of the American Mathematical Society

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

 
 

 

Wandering out to infinity of diffusion processes


Author: Avner Friedman
Journal: Trans. Amer. Math. Soc. 184 (1973), 185-203
MSC: Primary 60J60
DOI: https://doi.org/10.1090/S0002-9947-1973-0341631-5
MathSciNet review: 0341631
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Abstract: Let $ \xi (t)$ be a diffusion process in $ {R^n}$, given by $ d\xi = b(\xi )dt + \sigma (\xi )dw$. Conditions are given under which either $ \vert\xi (t)\vert \to \infty $ as $ t \to \infty $ with probability 1, or $ \xi (t)$ visits any neighborhood at a sequence of times increasing to infinity, with probability 1. The results are obtained both in case (i) $ \sigma (x)$ is nondegenerate, and (ii) $ \sigma (x)$ is degenerate at a finite number of points and hypersurfaces.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1973-0341631-5
Keywords: Brownian motion, stochastic differential equations, nondegenerate diffusion, degenerate diffusion, hitting time, fundamental solution of parabolic equation
Article copyright: © Copyright 1973 American Mathematical Society

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