Optimal Hoeffding bounds for discrete reversible Markov chains
Carlos A. Leon, Francois Perron
Abstract
We build optimal exponential bounds for the probabilities of large deviations of sums Σk=1nf(Xk) where (Xk) is a finite reversible Markov chain and f is an arbitrary bounded function. These bounds depend only on the stationary mean Eπf, the end-points of the support of f, the sample size n and the second largest eigenvalue λof the transition matrix.
Create a lesson
Related papers
Sublinear multi-type preferential attachment
Anna Ben-Hamou, Nicolas Broutin, Camille Cazaux
Uniform Central Limit Theorems for Degree Distributions of Sparse Graphon Models
Robert Lunde, Soumendra Lahiri
Matching Random Point Sets with Minimum Distortion
Itai Benjamini, Mark Braverman, Elad Tzalik et al.
Uniqueness and full coverage in k-neighbor graphs
David Coupier, Benoît Henry, Benedikt Jahnel et al.
Bass martingales need not stretch
Mathias Beiglböck, Manuel Hasenbichler, Gudmund Pammer
Universality of smallest singular values of random row submatrices and phase retrieval problems
Shu Wen, Christian E. Häggblom, Xiufan Yang