Articlegold1996

Moderate Deviations for Martingales with Bounded Jumps

59 citations0/0 files storedElectronic Communications in Probability

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Stochastic processes and financial applications Probability and Statistical Research Stochastic processes and statistical mechanics

Abstract

We prove that the Moderate Deviation Principle (MDP) holds for the trajectory of a locally square integrable martingale with bounded jumps as soon as its quadratic covariation, properly scaled, converges in probability at an exponential rate. A consequence of this MDP is the tightness of the method of bounded martingale differences in the regime of moderate deviations.

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References

1987Limit Theorems for Stochastic Processes 1989Theory of Martingales

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2009Deviation inequalities and moderate deviations for estimators of parameters in an Ornstein-Uhlenbeck process with linear drift 1999Large deviations, moderate deviations, and queues with long-range dependent input

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