An error term in the Central Limit Theorem for sums of discrete random variables.
(with Dmitry Dolgopyat) (submitted)
We consider sums of independent identically distributed random variables those distributions have d+1 atoms. Such distributions never admit an Edgeworth expansion of order d but we show that for almost all parameters the Edgeworth expansion of order d-1 is valid and the error of the order d-1 Edgeworth expansion is typically of order n^(-d/2).
Edgeworth expansions for weakly dependent random variables.
(with Carlangelo Liverani) (in preparation)
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. We primarily use spectral techniques to obtain the results.