Ergodicity in a sense of weak convergence, equilibrium-type identities and large deviations for Markov chains

2018 ◽  
Vol 19 (10) ◽  
pp. 3197-3238 ◽  
Author(s):  
Lorenzo Bertini ◽  
Raphael Chetrite ◽  
Alessandra Faggionato ◽  
Davide Gabrielli

1971 ◽  
Vol 11 (3) ◽  
pp. 607-625
Author(s):  
E. Misevičius

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


1991 ◽  
Vol 4 (4) ◽  
pp. 293-303
Author(s):  
P. Todorovic

Let {ξn} be a non-decreasing stochastically monotone Markov chain whose transition probability Q(.,.) has Q(x,{x})=β(x)>0 for some function β(.) that is non-decreasing with β(x)↑1 as x→+∞, and each Q(x,.) is non-atomic otherwise. A typical realization of {ξn} is a Markov renewal process {(Xn,Tn)}, where ξj=Xn, for Tn consecutive values of j, Tn geometric on {1,2,…} with parameter β(Xn). Conditions are given for Xn, to be relatively stable and for Tn to be weakly convergent.


1982 ◽  
Vol 19 (02) ◽  
pp. 272-288 ◽  
Author(s):  
P. J. Brockwell ◽  
S. I. Resnick ◽  
N. Pacheco-Santiago

A study is made of the maximum, minimum and range on [0,t] of the integral processwhereSis a finite state-space Markov chain. Approximate results are derived by establishing weak convergence of a sequence of such processes to a Wiener process. For a particular family of two-state stationary Markov chains we show that the corresponding centered integral processes exhibit the Hurst phenomenon to a remarkable degree in their pre-asymptotic behaviour.


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