Vassili Kolokoltsov: Stochastic monotonicity and duality

We shall develop a general approach to the analysis of duality of Markov process in the sense of $Ef(X_t^x-y)=Ef(x-Y_t^y)$ for a function $f$. This leads, on the one hand side, to the indepth analysis of duality arising from general ordering (St Mathew's principle), and, on the other side, to some remarkable identities for diffusions and stable-like processes.