A Special Model Of Random Walk On The Plane

The random walks have been widely studied and applied in many fields such as physical science, economics and etc. By now many kinds of random walk models such as simple random walks, symmetric random walks, and lattice random walks have been proposed and investigated. But most existing models of random walk are infinite step random walk, and considered limit behavior. Based on a gambling game, a model of finite step the random walk with absorbent boundaries on the plan is constructed and investigated. Using generating function and recurrence relation, some results about the probability of walking from the original point to absorbent boundaries are achieved from special situation to general situation.