A generalization of Cram\'{e}r large deviations for martingales

TL;DR

This paper extends Cramér's large deviation principles to martingales, providing a broader theoretical framework using change of measure techniques, supplementing prior work in stochastic processes.

Contribution

It introduces a generalized large deviation result for martingales, expanding the applicability of Cramér's theorem with a novel proof method.

Findings

Generalization of Cramér's large deviations for martingales

Uses change of measure technique for proof

Enhances theoretical understanding of martingale deviations

Abstract

In this note, we give a generalization of Cram\'{e}r's large deviations for martingales, which can be regarded as a supplement of Fan, Grama and Liu (Stochastic Process. Appl., 2013). Our method is based on the change of probability measure developed by Grama and Haeusler (Stochastic Process. Appl., 2000).