Edgeworth expansions for weakly dependent random variables
K.V. Fernando, Carlangelo Liverani
Abstract
We discuss sufficient conditions that guarantee the existence of asymptotic expansions for the CLT for weakly dependent random variables including observations arising from sufficiently chaotic dynamical systems like piece-wise expanding maps, and strongly ergodic Markov chains. As a corollary we obtain refinements of the Local Limit Theorem and moderate deviation results. We primarily use spectral techniques to obtain the results.
Topics & Concepts
Ergodic theoryCentral limit theoremStatistical physicsMathematicsChaoticMarkov chainLimit (mathematics)Random variableApplied mathematicsDynamical systems theoryPure mathematicsMathematical analysisPhysicsComputer scienceStatisticsQuantum mechanicsArtificial intelligenceMathematical Dynamics and FractalsStochastic processes and statistical mechanicsGeometry and complex manifolds