  Diffusion processes with branching play an important role in statistical
dynamics. They are a common approach to the computing of quantum mechanical
groundstates, and serve as models for population dynamics and as physical
pictures for biological evolution.
  On a computer the efficiency of this simulation method is limited by the
approach to the infinitesimal time step, which is necessary to perform
alternating diffusion and branching steps.
  In this paper, a method is described, which eliminates the infinitesimal time
step for a certain class of branching processes, if the process of interest can
be ``embedded'' into another process, which is solvable by other analytic
and/or numerical methods. The simplest choice for the embbeding process is
given by a process with a constant branching rate, which dominates the rate of
the embedded process.
