A generalised random walk is given by

dS = a(x, t)dt + b(x, t)dW

where a(x, t), b(x, t) are given functions of space and time and dW is a Weiner process i.e. W = and is a random number normally distributed with a mean of 0 and a variance of 1.

Simulate this random walk in 1 dimension with your own choice of a(x, t) and b(x, t) (you may choose to keep these constant, e.g. a=1). Estimate the expected value for your walk after 2500 steps.