Conditioned random walks: Part II

I will continue my discussion of the problem of conditioning a random walk on both its initial and final position. I will remind us of the main results obtained so far, and focus in this talk on the problem of identifying a stochastic differential equation that generates paths from the conditioned ensemble with the correct probability (an application of “Doob conditioning”). I will also discuss the distinction between average paths and optimal paths, which typically are not the same. Finally, if time permits, I will sketch out what I have established so far for the case of a neutral model of evolution (the Wright-Fisher and related models) in this context.