Abstract

In a diffusion model, given by a one dimensional stochastic differential equation, it is of interest to find the probability of absorption at zero. We show that the probability of absorption during any time is positive, and find the probability of ultimate absorption. The results are derived by martingale techniques. This model appears in applications as Branching diffusion in biology and Constant Elastisity of Variance model in finance.
 

Convenor:Aidan Sudbury