Bernstein-type inequalities for Markov chains and Markov processes: A simple and robust proof
Abstract
We establish a new Bernstein-type deviation inequality for general (non-reversible) discrete-time Markov chains via an elementary approach. More robust than existing works in the literature, our result only requires the Markov chain to satisfy an iterated Poincaré inequality. Moreover, our method can be readily generalized to continuous-time Markov processes.
Fields of Study & Subjects
Probability and Statistical Research
Markov Chains and Monte Carlo Methods
Stochastic processes and statistical mechanics
Publication details
- Journal / source
- Bernoulli
- Volume
- 32
- Issue
- 2
- Pages
- 1267–1284
- Publication date
- 29 January 2026