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
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