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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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Submitted on : Wednesday, June 27, 2012 - 12:17:01 PM
Last modification on : Tuesday, January 11, 2022 - 5:56:07 PM
Long-term archiving on: : Thursday, December 15, 2016 - 7:23:42 PM


  • HAL Id : tel-00712572, version 1



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



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