**Abstract:** |
We discuss a general class of stochastic processes obtained from a
given Markov process whose behavior is modified upon contact with
a catalyst, from the perspective of a particle system that undergoes branching with conservation of mass (Fleming-Viot mechanism). In the F-V case for diffusions with hard catalyst (equal to the boundary of an open set), one of the most difficult questions is whether the system is non-explosive, which is proven for non smooth domains, including Lipschitz. It is also shown that, with probability one, exactly one ancestry line survives for all times. We explain the relation of the process and its scaling limits to the existence of quasi-stationary distributions and their simulation. |