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July 2016 Smoluchowski–Kramers approximation and large deviations for infinite-dimensional nongradient systems with applications to the exit problem
Sandra Cerrai, Michael Salins
Ann. Probab. 44(4): 2591-2642 (July 2016). DOI: 10.1214/15-AOP1029

Abstract

In this paper, we study the quasi-potential for a general class of damped semilinear stochastic wave equations. We show that as the density of the mass converges to zero, the infimum of the quasi-potential with respect to all possible velocities converges to the quasi-potential of the corresponding stochastic heat equation, that one obtains from the zero mass limit. This shows in particular that the Smoluchowski–Kramers approximation is not only valid for small time, but in the zero noise limit regime, can be used to approximate long-time behaviors such as exit time and exit place from a basin of attraction.

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Sandra Cerrai. Michael Salins. "Smoluchowski–Kramers approximation and large deviations for infinite-dimensional nongradient systems with applications to the exit problem." Ann. Probab. 44 (4) 2591 - 2642, July 2016. https://doi.org/10.1214/15-AOP1029

Information

Received: 1 March 2014; Revised: 1 April 2015; Published: July 2016
First available in Project Euclid: 2 August 2016

zbMATH: 1350.60054
MathSciNet: MR3531676
Digital Object Identifier: 10.1214/15-AOP1029

Subjects:
Primary: 35K57, 49J45, 60F10, 60H15

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.44 • No. 4 • July 2016
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