Within the four-sided boundaries of x = 0, y = 0, x = m and, y = n, a two-dimensional random walk begins at integer-valued coordinates (h,k) and moves one unit on each step either up, down, left, or right with non-zero probabilities that sum to 1. The process stops when hitting a boundary. Let P(U), P(D), P(L) and P(R) be the probabilities of hitting the upper, the lower, the left, and the right boundary first, respectively, when starting from a specific initial point within the boundaries. We use a Markov-Chain method to compute these probabilities. Let xi,j be the probability of hitting the left boundary first, when starting at coordinates (i,j). We use a System of Equations method to find xi,j simultaneously for all possible starting points (i,j).
Advisor(s) or Committee Chair
Dr. David Neal
Wright, Miky, "Four-Sided Boundary Problem for Two-Dimensional Random Walks" (2013). Mahurin Honors College Capstone Experience/Thesis Projects. Paper 425.