Stability of maxima of random variables defined on a Markov chain
- 1 August 1972
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 4 (2) , 285-295
- https://doi.org/10.2307/1426000
Abstract
Consider maxima Mn of a sequence of random variables defined on a finite Markov chain. Necessary and sufficient conditions for the existence of normalizing constants Bn such that are given. The problem can be reduced to studying maxima of i.i.d. random variables drawn from a finite product of distributions πi=1mHi(x). The effect of each factor Hi(x) on the behavior of maxima from πi=1mHi is analyzed. Under a mild regularity condition, Bn can be chosen to be the maximum of the m quantiles of order (1 - n-1) of the H's.Keywords
This publication has 7 references indexed in Scilit:
- Tail equivalence and its applicationsJournal of Applied Probability, 1971
- Limit laws for maxima of a sequence of random variables defined on a Markov chainAdvances in Applied Probability, 1970
- Limit Theorems for Markov Renewal ProcessesThe Annals of Mathematical Statistics, 1964
- A Law of Large Numbers for the Maximum in a Stationary Gaussian SequenceThe Annals of Mathematical Statistics, 1962
- Markov Renewal Processes: Definitions and Preliminary PropertiesThe Annals of Mathematical Statistics, 1961
- The asymptotic behavior of the minimum in a sequence of random variablesDuke Mathematical Journal, 1949
- Sur La Distribution Limite Du Terme Maximum D'Une Serie AleatoireAnnals of Mathematics, 1943