Some joint distributions for Markov process (Q674671)

We study the joint distributions of four random variables \(h(\omega)\) (stopping time or optional time), location \(x(h)\), \(l(\omega)\) (co-optional time) and location \(x(l)\) for Markov processes. Some distributions for \(d(\geq 3)\)-dimensional Brownian motion and the joint distribution of first exit and last exit locations for symmetric stable processes are found.