Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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


Author: Muruhan Rathinam
Journal: Quart. Appl. Math. 73 (2015), 347-364
MSC (2010): Primary 60J27
DOI: https://doi.org/10.1090/S0033-569X-2015-01372-7
Published electronically: March 17, 2015
MathSciNet review: 3357498
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Abstract: We consider time homogeneous Markov processes in continuous time with state space $ \mathbb{Z}_{+}^{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 \mathbb{N}$ for all $ 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 $ \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 $ \nu _j$.


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Additional Information

Muruhan Rathinam
Affiliation: University of Maryland Baltimore County, Department of Mathematics and Statistics, Baltimore, Maryland 21250
Email: muruhan@umbc.edu

DOI: https://doi.org/10.1090/S0033-569X-2015-01372-7
Received by editor(s): May 28, 2013
Published electronically: March 17, 2015
Additional Notes: The research of this author was supported by grant NSF DMS-0610013
Article copyright: © Copyright 2015 Brown University
The copyright for this article reverts to public domain 28 years after publication.


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