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

• DOI: 10.1007/s11009-019-09703-x
• Publication Date: 2019-03-05T05:04:07Z
• Authors: Lei Gao; Dong Han
• Keywords: 0101 mathematics; 01 natural sciences

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.