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

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 $E(\Vert X(t){\Vert }^r)$ of all orders $r \in \nat$ for all $t\ge 0$. 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 ${\nu }_1,\dots ,{\nu }_M$. 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 ${\nu }_j$.

References in corpus (1)

• A scalable computational framework for establishing long-term behavior of stochastic reaction networks