h-transform of Doob and nonlocal branching processes.

We study the h-transform of Doob for nonlocal branching processes, we show that the branching property is preserved provided that h is a coherent state, and we emphasize the probabilistic representation of the solution to the associated nonlinear evolution equation. The tools are from the analytic and probabilistic potential theory. We also investigate the h-transform of a subordinate C 0 -semigroup of sub-Markovian operators on an L p space. [ABSTRACT FROM AUTHOR]