Stanislav Volkov

Polya urn model with removals, or linear competition process

We consider a stochastic model for the competition between various species, in which the number of particular species increases with a linear rate, and at the same time decreases with the rate given by arbitrary linear function of the other species. Should the number of species becomes zero at some point of time, it will stay zero (this species becomes extinct). We show that eventually only a random subset of non-interacting species survives. A similar result also holds for the relevant generalized Polya urn model with removals.