A Model Of Random Walk On The Plane And Its Computer Simulation

The random walks have received many researchers'attention, and have been widely applied in many fields such as physical science, chemistry, biology, economics and etc. Owing to our finite real world, many restricted random walks, such as symmetric random walks, random walks with absorbent boundaries, random walks with reflecting boundaries have been investigated deeply. In this paper, based on a gambling game, a model of finite step random walk with bilateral absorption barriers is constructed and investigated. Using generating function, the formulas of combination and recursion relation, a series of probability formula of particle from the original point to the bilateral absorption barriers and finish line is showed and proved by special situation to general situation. Considering the finite model and no discuss its limit process, we provide some graphs of computer simulation for the random walk, by the graphs we can find the regularity of the probability in the random walk model.