I am searching for a reference about conditioning a Markov process in the sense of Doob, i.e. using h-transforms. My particular concern is to condition a discrete-time Markov Process on a possibly null-measure event, and I would need results such as conditions for uniqueness of extremal harmonic functions , maybe results related to Green's functions...
I found :
- The (big) book of Doob, Classical potential theory and its probabilistic counterpart which is very general and would need a substantial investment to be understood.
- The book of Rogers and Williams Diffusions, Markov processes and martingales, which is not very detailed, and mainly deals with the continuous time case.
- Draft notes of A Bloemendal on the net http://www.math.harvard.edu/~alexb/rm/Doob.pdf
- Some explanations in an article of O'Connel Conditioned random walks and RSK correspondence http://homepages.warwick.ac.uk/~masgas/pubs/noc03a.pdf
Anyone would have an other idea ?