Extreme Value Distributions for Two Kinds of Path Sums of Markov Chain

Abstract

We consider the extreme value distributions for two kinds of path sums on condition that every path is a discrete time, homogeneous and irreducible ergodic Markov chain with a finite number of states. We not only derive the extreme value distribution for the first kind but also establish the equivalence of limit distributions of a sum and of a maximum sum for the second kind. Numerical experiments are conducted to confirm our results.