DEVIATION BOUNDS FOR ADDITIVE FUNCTIONALS OF MARKOV PROCESSES

By Patrick Cattiaux, Arnaud Guillin. 2006

73 citations recorded by the source corpus.

In this paper we derive non asymptotic deviation bounds for P� � � � 1 Z t 0 V (X s)ds Z V dµ � � � R � where X is a µ stationary and ergodic Markov process and V is some µ integrable function. These bounds are obtained under various moments assumptions for V , and various regularity assumptions for µ. Regularity means here that µ may satisfy various functional inequalities (F-Sobolev, generalized Poincare etc...).

Subfields: Finance, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ff4e7548a76cabb6ca55e045bb5a1bd55c06a7be

How researchers see this paper

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

In Finance

1. Arnaud Guillin
2. Patrick Cattiaux
3. A. Joulin
4. Pierre-André Zitt
5. Christian Léonard
6. Nian Yao
7. Feng-Yu Wang
8. D. Bakry

In Numerical Analysis

1. Arnaud Guillin
2. Pierre-André Zitt
3. Patrick Cattiaux
4. Liming Wu
5. A. Joulin
6. Christian Léonard

In Statistics and Probability

1. Arnaud Guillin
2. Patrick Cattiaux
3. Christian Léonard
4. Pierre-André Zitt
5. Liming Wu
6. A. Joulin
7. Nian Yao
8. Nathael Gozlan

Citations in the corpus

• Transportation-information inequalities for Markov processes (2007, result): “tly the inequality TΦIor W1I(c) with 4c2 = cP,and (3.3) is a direct consequence of (3.2) and Corollary 2.4-(1-d). (ii) Hoeffding type inequality (3.3) improves a similar result by Cattiaux and Guillin [8]. Lezaud [28] proved a deviation inequality, which is better than (3.3) in the moderate deviation”
• Poincaré inequalities and hitting times (2010, methodology): “The mixing rate is connected to the rate of convergence to equilibrium of the semi group, as explained in [13].”
• A new Poisson-type deviation inequality for Markov jump processes with positive Wasserstein curvature (2009, background): “…on (1.1), provided the stationary distribution π satisfies some functional inequalities such as Poincaré, log-Sobolev or transportation-type inequalities; see, for instance, the recent articles of Cattiaux and Guillin (2008), Djellout et al. (2004), Gourcy and Wu (2006) or Guillin et al. (2009).”
• Bernstein type's concentration inequalities for symmetric Markov processes (2010, unknown): “(1.1)”