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 be a diffusion process in , given by . Conditions are given under which either as with probability 1, or visits any neighborhood at a sequence of times increasing to infinity, with probability 1. The results are obtained both in case (i) is nondegenerate, and (ii) 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