We present, in the simplest possible form, the so called {\em martingale problem} strategy to establish limit theorems. The presentation is specially adapted to problems arising in partially hyperbolic dynamical systems. We will discuss a simple partially hyperbolic example with fast-slow variables and use the martingale method to prove an averaging theorem and study fluctuations from the average. The emphasis is on ideas rather than on results. Also, no effort whatsoever is done to review the vast literature of the field.

De Simoi, J., Liverani, C. (2015). The Martingale approach after Varadhan and Dolpogpyat. In P. Dolgopyat (a cura di), Hyperbolic Dynamics, Fluctuations and Large Deviations. Proceedings of Symposia in Pure Mathematics, 89, AMS (pp. 311-339). American Mathematical Society [http://dx.doi.org/10.1090/pspum/089].

The Martingale approach after Varadhan and Dolpogpyat

LIVERANI, CARLANGELO
2015-01-01

Abstract

We present, in the simplest possible form, the so called {\em martingale problem} strategy to establish limit theorems. The presentation is specially adapted to problems arising in partially hyperbolic dynamical systems. We will discuss a simple partially hyperbolic example with fast-slow variables and use the martingale method to prove an averaging theorem and study fluctuations from the average. The emphasis is on ideas rather than on results. Also, no effort whatsoever is done to review the vast literature of the field.
2015
Settore MAT/07 - FISICA MATEMATICA
English
Rilevanza internazionale
Capitolo o saggio
dynamical systems, partially hyperbolic, limit laws
De Simoi, J., Liverani, C. (2015). The Martingale approach after Varadhan and Dolpogpyat. In P. Dolgopyat (a cura di), Hyperbolic Dynamics, Fluctuations and Large Deviations. Proceedings of Symposia in Pure Mathematics, 89, AMS (pp. 311-339). American Mathematical Society [http://dx.doi.org/10.1090/pspum/089].
De Simoi, J; Liverani, C
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/113797
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