Finite / Countable State Space Stochastic Processes : Point Processes: Characterization of Associated Auto-Correlation Functions:

Abstract

In this research paper, the relationship between finite / countable state space stochastic processes and point processes is explored. Utilizing the known relationship between Poisson processes and continuous time Markov chains, finite / countable state space random processes are related to continuous time Markov Chains. Based on the known results for binary random processes, characterization of auto-correlation function of finite state space random processes is explored. An important characterization of corner positive definite matrices is provided.