Event Type:

Mathematical Biology Seminar

Date/Time:

Wednesday, October 19, 2011 - 09:00 to 10:00

Location:

STAG 222

Event Link:

Abstract:

In the Mathematical Biology seminar on 10/12/2011 a very broad generalization of the Lotka-Volltera

equation was considered, and one particular case was seen to have many

biologically and mathematically desirable properties. Specifically, it

was seen to be a transformation of an affine linear process, and as such

it was seen to possess an explicit solution.

This week we consider ways of generalizing this deterministic model

to a stochastic one (deterministic evolution not being a trait one normally

associates with biological systems). By analogy with the Square Root

Model, we seek a biological model that is the square of a stochastic

process having affine linear drift. Conditions on the diffusion term

that will ensure the squared process remains markov are investigated, as

is one possible method of coefficient inference.

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