Nash estimates and the asymptotic behavior of diffusions

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Publication Type Journal Article
School or College College of Science
Department Mathematics
Creator Golden, Kenneth M.
Other Author Goldstein, S.; Lebowitz, J . L.
Title Nash estimates and the asymptotic behavior of diffusions
Date 1988
Description In order to analyze the asymptotic behavior of a particle diffusing in a drift field derived from a smooth bounded potential, we develop Nash-type a priori estimates on the transition density of the process. As an immediate consequence of the estimates, we find that for a rapidly decaying potential in Rd, the mean squared displacement behaves like td + C(t), where C(t) (the time integral of the "velocity autocorrelation function") decays like t-d/2. We also prove, using the estimates, that for a potential in Rd of the form V + B, where V is stationary random ergodic and B has compact support, the diffusion converges under space and time scaling to the same Brownian motion as does the diffusion with B = 0.
Type Text
Publisher Institute of Mathematical Statistics
Volume 16
Issue 3
First Page 1127
Last Page 1146
Subject Potentials; Transition; Divergence
Language eng
Bibliographic Citation Golden, K. M., Goldstein, S., & Lebowitz, J . L. (1988). Nash estimates and the asymptotic behavior of diffusions. Annals of Probability, 16(3), 1127-46.
Rights Management (c)Institute of Mathematical Statistics
Format Medium application/pdf
Format Extent 879,866 bytes
Identifier ir-main,5717
ARK ark:/87278/s6jw8zhs
Setname ir_uspace
Date Created 2012-06-13
Date Modified 2012-06-13
ID 706852
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