This work shows how exponential concentration inequalities for additive functionals of stochastic processes over a finite time interval can be derived from concentration inequalities for martingales. The approach is entirely probabilistic and naturally includes time-inhomogeneous and non-stationary processes as well as initial laws concentrated on a single point. The class of processes studied includes martingales, Markov processes and general square integrable càdlàg processes. The general approach is complemented by a simple and direct method for martingales, diffusions and discrete-time Markov processes. The method is illustrated by deriving concentration inequalities for the Polyak–Ruppert algorithm, SDEs with time-dependent drift coefficients “contractive at infinity” with both Lipschitz and squared Lipschitz observables, some classical martingales and non-elliptic SDEs.

这项工作表明如何在有限的时间间隔内从随机过程的additive不等式中得出随机过程的加成函数的指数浓度不等式。该方法完全是概率性的，自然包括时间非均匀和非平稳过程以及集中在单个点上的初始定律。研究的过程类型包括mar，马尔可夫过程和一般平方可积càdlàg过程。通用方法由diffusion，扩散和离散时间马尔可夫过程的简单直接方法加以补充。通过推导Polyak-Ruppert算法的浓度不等式，Lipschitz和平方Lipschitz观测值具有随时间变化的漂移系数“无穷大”的SDE来说明该方法，