Moderate Deviations for Martingales with Bounded Jumps
نویسنده
چکیده
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.
منابع مشابه
On Concentration and Revisited Large Deviations Analysis of Binary Hypothesis Testing
This paper first introduces a refined version of the Azuma-Hoeffding inequality for discrete-parameter martingales with uniformly bounded jumps. The refined inequality is used to revisit the large deviations analysis of binary hypothesis testing.
متن کاملIRWIN AND JOAN JACOBS CENTER FOR COMMUNICATION AND INFORMATION TECHNOLOGIES Tightened Exponential Bounds for Discrete Time, Conditionally Symmetric Martingales with Bounded Jumps
This letter derives some new exponential bounds for discrete time, real valued, conditionally symmetric martingales with bounded jumps. The new bounds are extended to conditionally symmetric sub/ supermartingales, and are compared to some existing bounds.
متن کاملTightened Exponential Bounds for Discrete Time, Conditionally Symmetric Martingales with Bounded Jumps
This letter derives some new exponential bounds for discrete time, real valued, conditionally symmetric martingales with bounded jumps. The new bounds are extended to conditionally symmetric sub/ supermartingales, and are compared to some existing bounds. AMS 2000 subject classifications: 60F10, 60G40, 60G42.
متن کاملModerate Deviations 13
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 diierences in the regime of moderate deviations.
متن کاملOptimal Novikov-type criteria for local martingales with jumps
We consider càdlàg local martingales M with initial value zero and jumps larger than a for some a larger than or equal to −1, and prove Novikov-type criteria for the exponential local martingale to be a uniformly integrable martingale. We obtain criteria using both the quadratic variation and the predictable quadratic variation. We prove optimality of the coefficients in the criteria. As a coro...
متن کامل