Doob's h-transform

Summary

Doob's h-transform changes the transition probabilities of a Markov process by weighting them with a positive excessive function $h$. The new process, the h-process, behaves like the old one conditioned on an event described by $h$. Typical events are leaving a domain at a given boundary point or never being killed. It links positive harmonic functions, the Martin boundary, and conditioned processes.