3 papers
math.PR2024
Self-normalized Cramér-type Moderate Deviation of Stochastic Gradient Langevin Dynamics
Hongsheng Dai, Xiequan Fan, Jianya Lu
In this paper, we study the self-normalized Cramér-type moderate deviation of the empirical measure of the stochastic gradient Langevin dynamics (SGLD). Consequently, we also deriv…
math.PR2024
Deviation inequalities for contractive infinite memory processes
Paul Doukhan, Xiequan Fan
In this paper, we introduce a class of processes that contains many natural examples. The interesting feature of such type processes lays on its infinite memory that allows it to r…
math.PR2023
Self-normalized Cramér type moderate deviations for martingales and applications
Xiequan Fan, Qi-Man Shao
Cramér's moderate deviations give a quantitative estimate for the relative error of the normal approximation and provide theoretical justifications for many estimator used in stati…