Refine search
Actions for selected content:
1 results
Stability of maxima of random variables defined on a Markov chain
-
- Journal:
- Advances in Applied Probability / Volume 4 / Issue 2 / August 1972
- Published online by Cambridge University Press:
- 01 July 2016, pp. 285-295
- Print publication:
- August 1972
-
- Article
- Export citation
-
Consider maxima M n of a sequence of random variables defined on a finite Markov chain. Necessary and sufficient conditions for the existence of normalizing constants B n 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=1 m H i (x). The effect of each factor H i (x) on the behavior of maxima from πi=1 m H i is analyzed. Under a mild regularity condition, B n can be chosen to be the maximum of the m quantiles of order (1 - n -1) of the H's.
are given. The problem can be reduced to studying maxima of i.i.d. random variables drawn from a finite product of distributions π