Large deviations, moderate deviations, and the KLS conjecture

Moderate 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.

Delta Method in Large Deviations and Moderate Deviations for Estimators by Fuqing

The delta method is a popular and elementary tool for deriving limiting distributions of transformed statistics, while applications of asymptotic distributions do not allow one to obtain desirable accuracy of approximation for tail probabilities. The large and moderate deviation theory can achieve this goal. Motivated by the delta method in weak convergence, a general delta method in large devi...

Functional Large Deviations and Moderate Deviations for Markov-modulated Risk Models with Reinsurance

We establish a functional large deviation principle and a functional moderate deviation principle for Markov-modulated risk models with reinsurance by constructing an exponential martingale approach. Lundberg’s estimate of the ruin time is also presented.

Large and moderate deviations for matching problems and empirical discrepancies

We study the two-sample matching problem and its connections with the Monge-Kantorovich problem of optimal transportation of mass. We exploit this connection to obtain moderate and large deviation principles. For the classical problem on the unit square we present a conjecture which, if true, yields an explicit formula for the rate function.

Large Deviations