Stochastic vortices in periodically reclassified populations

Gracinda Rita Guerreiro; João Tiago Mexia

Discussiones Mathematicae Probability and Statistics (2008)

  • Volume: 28, Issue: 2, page 209-227
  • ISSN: 1509-9423

Abstract

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Our paper considers open populations with arrivals and departures whose elements are subject to periodic reclassifications. These populations will be divided into a finite number of sub-populations. Assuming that: a) entries, reclassifications and departures occur at the beginning of the time units; b) elements are reallocated at equally spaced times; c) numbers of new elements entering at the beginning of the time units are realizations of independent Poisson distributed random variables; we use Markov chains to obtain limit results for the relative sizes of the sub-populations corresponding to the states of the chain. Namely we will obtain conditions for stability of the relative sizes for transient and recurrent states as well as for all states. The existence of such stability corresponds to the existence of a stochastic structure based either on the transient or on the recurrent states or even on all states. We call these structures stochastic vortices because the structure is maintained despite entrances, departures and reallocations.

How to cite

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Gracinda Rita Guerreiro, and João Tiago Mexia. "Stochastic vortices in periodically reclassified populations." Discussiones Mathematicae Probability and Statistics 28.2 (2008): 209-227. <http://eudml.org/doc/277065>.

@article{GracindaRitaGuerreiro2008,
abstract = { Our paper considers open populations with arrivals and departures whose elements are subject to periodic reclassifications. These populations will be divided into a finite number of sub-populations. Assuming that: a) entries, reclassifications and departures occur at the beginning of the time units; b) elements are reallocated at equally spaced times; c) numbers of new elements entering at the beginning of the time units are realizations of independent Poisson distributed random variables; we use Markov chains to obtain limit results for the relative sizes of the sub-populations corresponding to the states of the chain. Namely we will obtain conditions for stability of the relative sizes for transient and recurrent states as well as for all states. The existence of such stability corresponds to the existence of a stochastic structure based either on the transient or on the recurrent states or even on all states. We call these structures stochastic vortices because the structure is maintained despite entrances, departures and reallocations. },
author = {Gracinda Rita Guerreiro, João Tiago Mexia},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {Markov chains; stochastic vortices},
language = {eng},
number = {2},
pages = {209-227},
title = {Stochastic vortices in periodically reclassified populations},
url = {http://eudml.org/doc/277065},
volume = {28},
year = {2008},
}

TY - JOUR
AU - Gracinda Rita Guerreiro
AU - João Tiago Mexia
TI - Stochastic vortices in periodically reclassified populations
JO - Discussiones Mathematicae Probability and Statistics
PY - 2008
VL - 28
IS - 2
SP - 209
EP - 227
AB - Our paper considers open populations with arrivals and departures whose elements are subject to periodic reclassifications. These populations will be divided into a finite number of sub-populations. Assuming that: a) entries, reclassifications and departures occur at the beginning of the time units; b) elements are reallocated at equally spaced times; c) numbers of new elements entering at the beginning of the time units are realizations of independent Poisson distributed random variables; we use Markov chains to obtain limit results for the relative sizes of the sub-populations corresponding to the states of the chain. Namely we will obtain conditions for stability of the relative sizes for transient and recurrent states as well as for all states. The existence of such stability corresponds to the existence of a stochastic structure based either on the transient or on the recurrent states or even on all states. We call these structures stochastic vortices because the structure is maintained despite entrances, departures and reallocations.
LA - eng
KW - Markov chains; stochastic vortices
UR - http://eudml.org/doc/277065
ER -

References

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  1. [1] F.R. Gantmacher, The Theory of Matrices, Vol. II, Chelsea, New York 1960. Zbl0088.25103
  2. [2] G. Guerreiro and J. Mexia, An Alternative Approach to Bonus Malus, Discussiones Mathematicae, Probability and Statistics 24 (2004), 197-213. Zbl1165.62349
  3. [3] M. Healy, Matrices for Statistics, Oxford Science Publications 1986. 
  4. [4] E. Parzen, Stochastic Processes, Holden Day, San Francisco 1962. 
  5. [5] T. Rolski, H. Schmidli, V. Schmidt and J. Teugels, Stochastic processes for insurance and finance, John Wiley & Sons 1999. Zbl0940.60005
  6. [6] J.R. Schott, Matrix Analysis for Statistics, New York, John Wiley and Sons, Inc., 1997. Zbl0872.15002

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