Hi:

Say I have a normalized distribution function that defines the likelihood of an object having some (x,y) position at time t. That is p(x,y,t) is the probability that the object is located at (x,y) at time t. I also have a normalized distribution function that defines the likelihood of this same object having some (vx, vy) velocity at time t. That is, p(vx,vy,t) is the probability that the velocity vector of this object is defined by (vx,vy). Say I know p(x,y,t), p(vx,vy,t) and p(vx,vy,t+dt). That is, I know the position distribution and velocity distribution at time t, as well as the velocity distribution at time t+dt. How do I advance the position distribution to p(x,y,t+dt)? Is this a convolution process? I'm really not sure how to approach the problem.

Thanks.