  Consider the mutually catalytic branching process with finite branching rate
$\gamma$. We show that as $\gamma\to\infty$, this process converges in
finite-dimensional distributions (in time) to a certain discontinuous process.
We give descriptions of this process in terms of its semigroup in terms of the
infinitesimal generator and as the solution of a martingale problem. We also
give a strong construction in terms of a planar Brownian motion from which we
infer a path property of the process. This is the first paper in a series or
three, wherein we also construct an interacting version of this process and
study its long-time behavior.
