Does increased stochasticity speed up extinction? (Q1605953)

The author considers a one-dimensional diffusion model describing the random evolution of the density of a population. Under biologically reasonable assumptions on the drift and diffusion coefficients, as functions of the population density, it is shown that the distribution of the time to extinction is stochastically decreasing by increasing the diffusion coefficient pointwise, while leaving the drift coefficient unchanged. The argument is based on convexity considerations.