Year: 2015
Type: article
Abstract: We consider time homogeneous Markov processes in continuous time with state space Z + N \mathbb {Z}_{+}^{N} and provide two sufficient conditions and one necessary condition for the existence of moments E ( ‖ X ( t ) ‖ r ) E(\|X(t)\|^r) of all orders r ∈ N r \in \mathbb {N} for all t ≥ 0 t \geq 0 . The sufficient conditions also guarantee an exponential in time growth bound for the moments. The class of processes studied has finitely many state independent jumpsize vectors ν 1 , … , ν M \nu _1,\dots ,\nu _M . This class of processes arises naturally in many applications such as stochastic models of chemical kinetics, population dynamics and epidemiology for example. We also provide a necessary and sufficient condition for stoichiometric boundedness of species in terms of ν j \nu _j .
Source: Quarterly of Applied Mathematics
Author: Muruhan Rathinam
Institution: University of Maryland, Baltimore County
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Funder: National Science Foundation
OpenAlex ID: W2168403922