On Certain Probability Models in Random Walk

Abstract

This paper considers a two dimensional random walk in which a particle moves from its position a unit step either horizontally, or vertically, or diagonally forward or stay there with respective probabilities p, q, r and s (p + q + r + s= 1). The probabilities that initially at (0, 0}, the position of the particle is (x, y) at time t+ 0 after having in the line y = x, (i) h crosses and (ii) g hits and b slips, have been determined alongwith their generating functions.