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September 2017 On the behavior of diffusion processes with traps
M. Freidlin, L. Koralov, A. Wentzell
Ann. Probab. 45(5): 3202-3222 (September 2017). DOI: 10.1214/16-AOP1134


We consider processes that coincide with a given diffusion process outside a finite collection of domains. In each of the domains, there is, additionally, a large drift directed towards the interior of the domain. We describe the limiting behavior of the processes as the magnitude of the drift tends to infinity, and thus the domains become trapping, with the time to exit the domains being exponentially large. In particular, in exponential time scales, metastable distributions between the trapping regions are considered.


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M. Freidlin. L. Koralov. A. Wentzell. "On the behavior of diffusion processes with traps." Ann. Probab. 45 (5) 3202 - 3222, September 2017.


Received: 1 October 2015; Revised: 1 April 2016; Published: September 2017
First available in Project Euclid: 23 September 2017

zbMATH: 06812203
MathSciNet: MR3706741
Digital Object Identifier: 10.1214/16-AOP1134

Primary: 35J25 , 47D07 , 60F10 , 60J60

Keywords: Exit problem , large deviations , Metastable distributions , nonstandard boundary problem

Rights: Copyright © 2017 Institute of Mathematical Statistics


Vol.45 • No. 5 • September 2017
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