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Abstrakty
In this note we show that for Z being a birth and death process on Z or Brownian motion with drift and (…), the speed of convergence to the quasi-stationary distribution is of order 1/t. The corresponding version that X is the number of calls in M/M/1 queue or the reflected Brownian motion is also considered. The result is obtained by asymptotic expansions of some transition functions. For this we use some new asymptotic expansion of the Bessel function.
Wydawca
Czasopismo
Rocznik
Tom
Strony
385--397
Opis fizyczny
Bibliogr. 8 poz.
Twórcy
autor
autor
- Mathematical Institute University of Wroclaw Pl. Grunwaldzki 2/4 50-384 Wroclaw, Poland, Mariusz.Polak@math.uni.wroc.pl
Bibliografia
- [1] M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards (1964).
- [2] S. Asmussen, Applied Probability and Queues, 2nd ed., Springer, New York (2003).
- [3] R. N. Bhattacharya, R. Ranga Rao, Normal Approximation and Asymptotic Expansions, Krieger Malabar, Florida (1986).
- [4] A. N. Borodin, P. Salminen, Handbook of Brownian Motion – Facts and Formulae, 2nd ed., Birkhäuser, Basel-Boston-Berlin (2002).
- [5] A. Kyprianou, Z. Palmowski, Quasi-stationary distributions for Lévy processes, Bernoulli 12(4) (2006), 571–581.
- [6] A. E. Kyprianou, Introductory Lectures on Fluctuations of Lévy Processes with Applications, Universitext, Springer (2006).
- [7] M. Mandjes, Z. Palmowski, T. Rolski, Quasi-stationary workload in a Lévy-driven storage system, submitted (2010).
- [8] S. Martinez, J. San Martin, Quasi-stationary distributions for a Brownian motion with drift and associated limit laws, J. Appl. Probab. 31 (1994), 911–920.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA4-0034-0034