Recent advances in invariance principles for stationary sequences.
Convolution property and exponential bounds for symmetric monotone densities
Our first theorem states that the convolution of two symmetric densities which are -monotone on (0∞) is again (symmetric) -monotone provided 0 ≤ 1. We then apply this result, together with an extremality approach, to derive sharp moment and exponential bounds for distributions having such shape constrained densities.
Moderate deviations for stationary sequences of bounded random variables
In this paper we derive the moderate deviation principle for stationary sequences of bounded random variables under martingale-type conditions. Applications to functions of -mixing sequences, contracting Markov chains, expanding maps of the interval, and symmetric random walks on the circle are given.
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