Suppose I have a large particle of mass [itex]M[/itex] that is randomly emitting small particles. The magnitude of the momenta of the small particles is [itex]\delta p[/itex] (and it is equal for all of them. Each particle is launched in a random direction (in 3 spatial dimensions--although we can work with 1 dimension if it's much easier). Assume also that these particles are emitted at a uniform rate with time [itex]\delta t[/itex] between emissions. So here's my issue. It seems to me that this is a random walk in momentum space. What I would like to know is how to estimate the displacement of the particle after [itex]N[/itex] particles are pooped out. Thus, I need some way to "integrate the velocity". However, I want to stress that I only care about an order of magnitude estimate of the displacement here. Has anyone dealt with this kind of a situation? I appreciate any help greatly!