Time Homogeneous Diffusion with drift and killing to meet a given marginal
arXiv:1307.3413
Abstract
This article gives conditions on a probability measure and drift field b such that for a given killing field k and a given time t > 0, there is function a such that there is a time homogeneous Markov process with infinitesimal generator a((1/2)d^2/dx^2 + b d/dx - k) which meets the given marginal at time t.