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2015 Quenched large deviations for multiscale diffusion processes in random environments
Konstantinos Spiliopoulos
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Electron. J. Probab. 20: 1-29 (2015). DOI: 10.1214/EJP.v20-3729


We consider multiple time scales systems of stochastic differential equations with small noise in random environments. We prove a quenched large deviations principle with explicit characterization of the action functional. The random medium is assumed to be stationary and ergodic. In the course of the proof we also prove related quenched ergodic theorems for controlled diffusion processes in random environments that are of independent interest. The proof relies entirely on probabilistic arguments, allowing to obtain detailed information on how the rare event occurs. We derive a control, equivalently a change of measure, that leads to the large deviations lower bound. This information on the change of measure can motivate the design of asymptotically efficient Monte Carlo importance sampling schemes for multiscale systems in random environments


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Konstantinos Spiliopoulos. "Quenched large deviations for multiscale diffusion processes in random environments." Electron. J. Probab. 20 1 - 29, 2015.


Accepted: 24 February 2015; Published: 2015
First available in Project Euclid: 4 June 2016

zbMATH: 1320.60081
MathSciNet: MR3317157
Digital Object Identifier: 10.1214/EJP.v20-3729

Primary: 60F10
Secondary: 60F99, 60G17, 60J60


Vol.20 • 2015
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