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July 2016 On large deviations of coupled diffusions with time scale separation
Anatolii A. Puhalskii
Ann. Probab. 44(4): 3111-3186 (July 2016). DOI: 10.1214/15-AOP1043


We consider two Itô equations that evolve on different time scales. The equations are fully coupled in the sense that all of the coefficients may depend on both the “slow” and the “fast” variables and the diffusion terms may be correlated. The diffusion term in the slow process is small. A large deviation principle is obtained for the joint distribution of the slow process and of the empirical process of the fast variable. By projecting on the slow and fast variables, we arrive at new results on large deviations in the averaging framework and on large deviations of the empirical measures of ergodic diffusions, respectively. The proof relies on the property that an exponentially tight sequence of probability measures on a metric space is large deviation relatively compact. The identification of the large deviation rate function is accomplished by analyzing the large deviation limit of an exponential martingale.


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Anatolii A. Puhalskii. "On large deviations of coupled diffusions with time scale separation." Ann. Probab. 44 (4) 3111 - 3186, July 2016.


Received: 1 February 2015; Revised: 1 May 2015; Published: July 2016
First available in Project Euclid: 2 August 2016

zbMATH: 1356.60047
MathSciNet: MR3531687
Digital Object Identifier: 10.1214/15-AOP1043

Primary: 60F10, 60J60
Secondary: 60F17, 60G57

Rights: Copyright © 2016 Institute of Mathematical Statistics


Vol.44 • No. 4 • July 2016
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