Hello,

I am looking for mathematical analysis for the following 2D random walk.

Starting from the origin or some location (x1,y1) in 2 dimensional space, what is the probability that a particle will reach a specified location (area), during a given time interval?

Any books or references? Thanks Lakshmi

Hello Steve,and others thanks.

I was not able to get reference on heat equation which was suggested earlier.

Also the links that was proposed on wike are general and nothing rigours for 2D discrete random walk.

As everyone asked about the question was not clear. All I am looking is analytical approach to solve the 2D, symmetric, unbiased,discrete random walk within a bounded first quadrant regions. The boundary are reflecting boundary. The particle starts at location (x1,y1) and the target is at location b (x2,y2), the particle has to reach within time interval "T".

The same condition i wanted to continuous random walk. The reflecting boundaries can be considered here as optional.

First i want to consider for unbounded 2-D random walk, Symmetric random walk. Then i want to consider bounded 1st quadrant random walk.