  A competition process is a continuous time Markov chain that can be
interpreted as a system of interacting birth-and-death processes, the
components of which evolve subject to a competitive interaction. This paper is
devoted to the study of the long-term behaviour of such a competition process,
where a component of the process increases with a linear birth rate and
decreases with a rate given by a linear function of other components. A zero is
an absorbing state for each component, that is, when a component becomes zero,
it stays zero forever (and we say that this component becomes extinct). We show
that, with probability one, eventually only a random subset of non-interacting
components of the process survives. A similar result also holds for the
relevant generalized Polya urn model with removals.
