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

Source: [Moment growth bounds on continuous time Markov processes on non-negative integer lattices](<https://www.sota2.com/research/paper/68fa51731e209131ce973e52>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T11:25:19.620Z

Authors: Muruhan Rathinam

Published: 2013-04-18T15:58:28.000Z

## 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 $r \\in \\nat$ for all $t \\geq 0$. 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 $\\nu\_j$.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1304.5169>)

[PDF](<https://arxiv.org/pdf/1304.5169.pdf>)