Hi, can someone who is familiar with the analysis of random walks (statistical mechanics, condensed matter physics etc.) help me on solving a particular problem? We define the following random walk, the random variable w(t) is evolved as w(t+1)=w(t), with probability of p; w(t+1)=w(t)+C*(1-w(t))*f, with probability 1-p. C is a constant, f is a random variable with known distribution, and f is not correlated with w. Following the way of analyzing a Brownian motion, what I have tried is to write down E(w(t)|w(t-1),p), then show the E(w(t)|p) using the induction, for a given w(0). Next, at least I need to find the Var(w(t)) , or equivalently E(w(t)^2) since I have known (E(w(t)))^2 for a given w(0). I hope that someone can help me find the moment generating function of this random walk (E(w(t)^n)), or alternatively just the mean and the variance of w(t). Any hint on this is badly needed.