Collisions of Markov Processes

Abstract

Let $X_1$ and $X_2$ be two independent Hunt processes which take values in a metric space and have the same transition density functions with respect to a reference measure. We describe explicit conditions on the transition density functions so that $X_1$ and $X_2$ have collisions with positive probability or with probability one or do not have any collision. The applications to Lévy processes, diffusions driven by s.d.e.'s and Brownian motions on fractals are exhibited.