Exact asymptotics of probabilities of large deviations for Markov chains: the Laplace method

2011 ◽  
Vol 75 (4) ◽  
pp. 837-868 ◽  
Author(s):  
Vadim R Fatalov
Keyword(s):  
Markov Chains ◽  
Large Deviations ◽  
Exact Asymptotics ◽  
Laplace Method ◽  
Probabilities Of Large Deviations

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

scholarly journals Asymptotics for the First Passage Times of Lévy Processes and Random Walks

2013 ◽  
Vol 50 (1) ◽  
pp. 64-84 ◽  
Author(s):  
Denis Denisov ◽  
Vsevolod Shneer
Keyword(s):  
Large Deviations ◽  
Random Walks ◽  
Levy Processes ◽  
Levy Process ◽  
First Passage Times ◽  
Exact Asymptotics ◽  
First Passage ◽  
Heavy Tailed ◽  
First Time ◽  
Passage Times

We study the exact asymptotics for the distribution of the first time, τx, a Lévy process Xt crosses a fixed negative level -x. We prove that ℙ{τx >t} ~V(x) ℙ{Xt≥0}/t as t→∞ for a certain function V(x). Using known results for the large deviations of random walks, we obtain asymptotics for ℙ{τx>t} explicitly in both light- and heavy-tailed cases.

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