Moment growth bounds on continuous time Markov processes on non-negative integer lattices

2013/04/18 by Rathinam, Muruhan
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1304.5169

Abstract

We consider Markov processes in continuous time with state space \posint^N and provide two sufficient conditions and one necessary condition for the existence of moments E(‖X(t)‖^r) of all orders r ∈ \nat for all t ≥ 0. The sufficient conditions also guarantee an exponential in time growth bound for the moments. The class of processes studied have finitely many state independent jumpsize vectors ν₁,…,ν_M. This class of processes arise naturally in many applications such as stochastic models of chemical kinetics, population dynamics and queueing theory for example. We also provide a necessary and sufficient condition for stochiometric boundedness of species in terms of ν_j.

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