Large Deviations for Empirical Measures of Not Necessarily Irreducible Countable Markov Chains with Arbitrary Initial Measures

2005 ◽  
Vol 21 (6) ◽  
pp. 1377-1390 ◽  
Author(s):  
Yi Wen Jiang ◽  
Li Ming Wu
Keyword(s):  
Markov Chains ◽  
Large Deviations ◽  
Empirical Measures

scholarly journals Extended Laplace principle for empirical measures of a Markov chain

2019 ◽  
Vol 51 (01) ◽  
pp. 136-167 ◽  
Author(s):  
Stephan Eckstein
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Large Deviations ◽  
Large Deviation ◽  
Dual Pair ◽  
Wasserstein Distance ◽  
Large Deviations Principle ◽  
Empirical Measures ◽  
Leibler Divergence ◽  
Laplace Principle

AbstractWe consider discrete-time Markov chains with Polish state space. The large deviations principle for empirical measures of a Markov chain can equivalently be stated in Laplace principle form, which builds on the convex dual pair of relative entropy (or Kullback– Leibler divergence) and cumulant generating functional f ↦ ln ʃ exp (f). Following the approach by Lacker (2016) in the independent and identically distributed case, we generalize the Laplace principle to a greater class of convex dual pairs. We present in depth one application arising from this extension, which includes large deviation results and a weak law of large numbers for certain robust Markov chains—similar to Markov set chains—where we model robustness via the first Wasserstein distance. The setting and proof of the extended Laplace principle are based on the weak convergence approach to large deviations by Dupuis and Ellis (2011).

scholarly journals Level 2.5 Large Deviations for Continuous-Time Markov Chains with Time Periodic Rates

2018 ◽  
Vol 19 (10) ◽  
pp. 3197-3238 ◽  
Author(s):  
Lorenzo Bertini ◽  
Raphael Chetrite ◽  
Alessandra Faggionato ◽  
Davide Gabrielli
Keyword(s):  
Markov Chains ◽  
Large Deviations ◽  
Continuous Time ◽  
Continuous Time Markov Chains ◽  
Time Periodic

scholarly journals Local theorems of large deviations for homogeneous Markov chains

1971 ◽  
Vol 11 (3) ◽  
pp. 607-625
Author(s):  
E. Misevičius
Keyword(s):  
Markov Chains ◽  
Large Deviations

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: Э. В. Мисевичюс. Локальные теоремы с большими уклонениями для однородных цепей Маркова E. Misevičius. Didelių nukrypimų lokalinės teoremos homogeninėms Markovo grandinėms

On large deviations of empirical measures in the τ-topology

1994 ◽  
Vol 31 (A) ◽  
pp. 41-47 ◽  
Author(s):  
A. De Acosta
Keyword(s):  
Large Deviations ◽  
State Space ◽  
The State ◽  
Probability Measures ◽  
Empirical Measures

We prove a generalization of Sanov's theorem in which the state space S is arbitrary and the set of probability measures on S is endowed with the τ -topology.

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