Random Walks as Markov Chains

Abstract

The dissertation applies the Markov chain theory to four types of random walks namely; simple random walk, random walk with reflecting barriers, random walks with absorbing barriers and cyclic random walks. Various methods of determining the nth power are employed where all methods yield the same results. The Computation of 2×2 transition probabilities provides results which are easily generalized. However, using the direct method of multiplication, it is difficult come up with a generalized pattern. The 3×3 transition probability matrices onwards give complex patterns which are not easy to generalize especially in the case of the cyclic random walks. The method of multiplication gives a visible pattern similar to that of the Pascal triangle, but the generalization of the nth term is difficult