Stationarity of a stochastic population flow model

Stadje, Wolfgang

doi:10.1239/jap/1032374251

Cited by 2 publications

(1 citation statement)

References 3 publications

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“…Open Markov chain schemes fed by a second order stationary and non-stationary processes have also been studied in [24] where the authors consider that the inflow of new population elements is modeled by a time series coming from a second order stationary process, i.e., a stationary process with a deterministic bias. Additionally, open Markov chains with not independent inflow processes has been considered in [25]. All these different models of stochastic open systems have been useful for several important applications.…”

Section: Introductionmentioning

confidence: 99%

Open Markov Chains: Cumulant Dynamics, Fluctuations and Correlations

Salgado-García

2021

Entropy

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In this work we propose a model for open Markov chains that can be interpreted as a system of non-interacting particles evolving according to the rules of a Markov chain. The number of particles in the system is not constant, because we allow the particles to arrive or leave the state space according to prescribed protocols. We describe this system by looking at the population of particles on every state by establishing the rules of time-evolution of the distribution of particles. We show that it is possible to describe the distribution of particles over the state space through the corresponding moment generating function. This description is given through the dynamics ruling the behavior of such a moment generating function and we prove that the system is able to attain the stationarity under some conditions. We also show that it is possible to describe the dynamics of the two first cumulants of the distribution of particles, which in some way is a simpler technique to obtain useful information of the open Markov chain for practical purposes. Finally we also study the behavior of the time-dependent correlation functions of the number of particles present in the system. We give some simple examples of open chains that either, can be fully described through the moment generating function or partially described through the exact solution of the cumulant dynamics.

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Section: Introductionmentioning

confidence: 99%