DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:**Muruhan Rathinam, Department of Mathematics and Statistics, UMBC

**Title: ***
Moment Growth Bounds on Markov Processes on Non-negative Integer
Lattices*

**Abstract:**
We consider the class of continuous time Markov processes with
the * N*-dimensional non-negative integer lattice as state space that have
finitely many state independent jumpsize vectors. Such processes in general
can be regarded as population processes modeling the vector copy number of
*N* different species undergoing $M$ different types of reaction/interaction
events. Typical examples of such processes are stochastically modeled
chemical
reactions, predator-prey models as well as epidemiological models. These
processes are uniquely characterized by their "propensity" functions as well
as their "stoichiometric vectors."
Such processes often possess the property that given a deterministic initial
condition the process always remains in a bounded region of the state space.
We provide a necessary and sufficient condition on the stoichiometric matrix
for this to hold. When the process is not bounded in the state space a
natural question is whether finite moments of all orders exist. We provide
two different sufficient conditions and one necessary condition for the
existence of moments of all orders for all time *t* > 0.

**Time:** Friday, October 18, 2013, 1:30-2:30 p.m.

**Place:** Exploratory Hall (formerly S & T II), Room 4106

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491