Stochastic vortices in periodically reclassified populations

• Autorzy: Gracinda Rita Guerreiro , João Tiago Mexia
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Markov chains; stochastic vortices

Kategorie tematyczne

• 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae Probability and Statistics
• Rocznik: 2008
• Tom: 28
• Numer: 2
• Strony: 209-227

Daty

wydano

2008

otrzymano

2007-11-20

poprawiono

2008-04-10

Twórcy

autor

Gracinda Rita Guerreiro

• Department of Mathematics, FCT - New University of Lisbon, Campus da Caparica, 2829-516 Caparica, Portugal

autor

João Tiago Mexia

• Department of Mathematics, FCT - New University of Lisbon, Campus da Caparica, 2829-516 Caparica, Portugal

Bibliografia

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

Identyfikatory

DOI

10.7151/dmps.1101