Stationary Distribution of Markov Chain

Abstract: Markov chain is a mathematical tool for modeling systems that evolve over time and hasbeen used in many fields such as physics, chemistry, economics, biology, and data science.This thesis contains an introduction to the theory and the applications of Markov chains,focusing on those with finite state spaces. Starting with basic concepts and techniques, thetheory of Markov chains is comprehensively studied. The basic concepts covered includethe Markov property, transition matrix, higher order transition probabilities, classification of states, and Markov chains as graphs. The stationary distribution, its importancein probability theory, existence, and uniqueness of stationary distribution are then discussed, while the final part of the thesis deals with the simulations of Markov chains. Twoexamples are presented to illustrate the technique of Markov chain simulation, includinga weather prediction model and a DNA sequence model.