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October, 1987 Metastability for a Class of Dynamical Systems Subject to Small Random Perturbations
Antonio Galves, Enzo Olivieri, Maria Eulalia Vares
Ann. Probab. 15(4): 1288-1305 (October, 1987). DOI: 10.1214/aop/1176991977


We consider dynamical systems in $\mathbb{R}^d$ driven by a vector field $b(x) = - \nabla a(x)$, where $a$ is a double-well potential with some smoothness conditions. We show that these dynamical systems when subjected to a small random disturbance exhibit metastable behavior in the sense defined in [2]. More precisely, we prove that the process of moving averages along a path of such a system converges in law when properly normalized to a jump Markov process. The main tool for our analysis is the theory of Freidlin and Wentzell [7].


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Antonio Galves. Enzo Olivieri. Maria Eulalia Vares. "Metastability for a Class of Dynamical Systems Subject to Small Random Perturbations." Ann. Probab. 15 (4) 1288 - 1305, October, 1987.


Published: October, 1987
First available in Project Euclid: 19 April 2007

zbMATH: 0709.60058
MathSciNet: MR905332
Digital Object Identifier: 10.1214/aop/1176991977

Primary: 60H10
Secondary: 60J05

Keywords: dynamical systems , large deviations , metastability

Rights: Copyright © 1987 Institute of Mathematical Statistics

Vol.15 • No. 4 • October, 1987
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