An Asymptotic Solution to a Two-Dimensional Exit Problem Arising in Population Dynamics

Source abstract

A study is made of a two-dimensional stochastic system with small stochastic fluctuations arising in population biology. At the boundary of the state space the diffusion matrix becomes singular. By an asymptotic analysis, expressions are derived that determine the probability of exit at each of the two boundaries and the expectation and variance of the exit time. These expressions contain constants that can be computed numerically.