String’s Approximation, Recurrence Theorem, Random walk
Abstract
Random walk is a randomly walk process that describes the path including a succession of random steps in the mathematical region. A procedure for estimating the likely position of a point exposed to random motions in probability theory, given the probabilities (which remain constant at each step) of traveling a certain distance in a certain direction. A Markov process that exhibits future behavior independent of prior history is the random walk. This paper will discover the classic recurrence Theorem concerning random walks on the d-dimensional integer lattice, and demonstrate the leads to complete generality with simple methods supported by String’s Approximation. Furthermore, this essay will explore the situation that walker randomly walks in different dimensions and discover that random walk on dimensions one and two will return to the initial point, dimension three and higher dimensions will not. The meaning of this essay is to help more people have some basic understanding with random walk and to know there are some applications of random walk.
