Bernstein type's concentration inequalities for symmetric Markov processes

By Fuqing Gao, Arnaud Guillin, Liming Wu. 2010

48 citations recorded by the source corpus.

Using the method of transportation-information inequality introduced in [A. Guillin et al., Probab. Theory Related Fields, 144 (2009), pp. 669--695], we establish Bernstein-type concentration inequalities for empirical means of functions of the Markov process $(\int_0^t g(X_s)\,ds)/t$ where $g$ is an unbounded observable of the symmetric Markov process $(X_t)$. Three approaches are proposed: a functional inequalities approach, a Lyapunov function method, and an approach through the Lipschitzian norm of the solution to the Poisson equation. Several applications and examples are studied.

Subfields: Applied Mathematics, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/cc20973701cd20841ac9e2994867e9afda28264e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Nathael Gozlan
2. Christian Léonard
3. Arnaud Guillin
4. Patrick Cattiaux
5. Cyril Roberto
6. Emmanuel Boissard

In Numerical Analysis

1. Christian Léonard
2. Nathael Gozlan

In Statistics and Probability

1. Nathael Gozlan
2. Christian Léonard

Citations in the corpus

• Transport Inequalities. A Survey (2010, background): “In [45], Gao, Guillin and Wu have refined the above concentration results in such a way that Bernstein inequalities are accessible.”