Event Type:

Mathematical Biology Seminar

Date/Time:

Thursday, March 14, 2013 - 06:00

Location:

WNGR 275

Event Link:

Guest Speaker:

Grant Thompson

Institution:

National Marine Fisheries Service (NOAA) & OSU Dept. of Fisheries and Wildlife

Abstract:

This talk reprises a 2011 presentation in which I described a model of ecological community dynamics involving square root transforms of species abundances, and describes work toward developing a stochastic version of that model. The basic (deterministic) square root model is a set of differential equations exhibiting several desirable features, including a closed-form solution. Ed Waymire, William Felder, and I have worked on generalizing this model to stochastic differential form. For the special case of a single dimension, the Feller diffusion process (popularized in the finance literature by Cox, Ingersoll, and Ross) presents an intriguing starting point for such a generalization, because the transition distribution can be written in closed form. Unfortunately, a closed-form solution for the transition distribution in higher dimensions does not exist. However, a method developed by Ait-Sahalia allows the transition distribution for the multivariate case to be approximated to any desired degree of precision. Because the transition distribution for the univariate case is available in closed form, it provides a convenient way to test the efficiency with which Ait-Sahalia’s method performs. If the technology in the classroom works, I will test Ait-Sahalia’s method in “real time” by generating several hypothetical examples based on randomly drawn parameter values