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Limit theorems for stationary processes

Abstract : We study the spectral measure for stationary transformations, and then apply to Ergodic theorem and Central limit theorem. We study also martingale process with a new proof of the central limit theorem without Fourier analysis. For the central limit theorem for random walks in random environment, we give two methods to obtain it: martingale approximation and moments. The method of martingales solves Dirichlet's equation (I −P )h = 0, and the method of moments solves Poisson's equation (I − P )h = f . Finally, we can use the second method to prove the Einstein relation for reversible diffusions in random environment in one dimension.
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https://tel.archives-ouvertes.fr/tel-00712572
Contributor : Hoang Chuong Lam <>
Submitted on : Wednesday, June 27, 2012 - 12:17:01 PM
Last modification on : Thursday, March 5, 2020 - 5:32:55 PM
Document(s) archivé(s) le : Thursday, December 15, 2016 - 7:23:42 PM

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  • HAL Id : tel-00712572, version 1

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Hoang Chuong Lam. Limit theorems for stationary processes. Probability [math.PR]. Université François Rabelais - Tours, 2012. English. ⟨tel-00712572⟩

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