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Boundary Problems For One And Two Dimensional Random Walks, Miky Wright
Boundary Problems For One And Two Dimensional Random Walks, Miky Wright
Masters Theses & Specialist Projects
This thesis provides a study of various boundary problems for one and two dimensional random walks. We first consider a one-dimensional random walk that starts at integer-valued height k > 0, with a lower boundary being the x-axis, and on each step moving downward with probability q being greater than or equal to the probability of going upward p. We derive the variance and the standard deviation of the number of steps T needed for the height to reach 0 from k, by first deriving the moment generating function of T. We then study two types of two-dimensional random walks with …