Averaging in Markov Models with Fast Semi-Markov Switches and Applications

Communications in Statistics - Theory and Methods

Volumn 33, Issue 3, 2004, Pages 517-531

  Anisimov, Vladimir V ^a  

^a GLAXOSMITHKLINE   (United Kingdom)

Author keywords

Averaging principle; Markov process; Multicentre trials; Queueing system; Semi Markov process; Switching process

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FUNCTIONS; LARGE SCALE SYSTEMS; MATHEMATICAL MODELS; SET THEORY; STOCHASTIC CONTROL SYSTEMS; SWITCHING; THEOREM PROVING;

QUEUEING SYSTEMS; SEMI-MARKOV PROCESSES;

MARKOV PROCESSES;

EID: 1642263723     PISSN: 03610926     EISSN: None     Source Type: Journal    
DOI: 10.1081/STA-120028682     Document Type: Article

References (13)

1. Anisimov, V. V. (1978). Applications of limit theorems for switching processes. Cybernetics 14(6):917-929.
2. Anisimov, V. V. (1995). Switching processes: Averaging principle, diffusion approximation and applications. Acta Applicandae Mathematicae 40:95-141.
3. Anisimov, V. V. (1999). Averaging methods for transient regimes in overloading retrial queuing systems. Math. Comput. Model. 30(3/4):65-78.
4. Anisimov, V. V. (2000). Asymptotic analysis of reliability for switching systems in light and heavy traffic conditions. In: Limnios, N., Nikulin, M., eds. Recent Advances in Reliability Theory: Methodology, Practice and Inference. Boston: Birkhäuser, pp. 119-133.
5. Anisimov, V. V. (2002). Averaging in Markov models with fast Markov switches and applications to queueing models. Annals of Operations Res. 112(1-4):63-82.
6. Anisimov, V. V., Fedorov, V. F., Jones, B. (2003). Analysis of recruitment time for multicentre clinical trials. In: Proc. of 6th UKSiM 2003 Conference. Cambridge, UK, April, pp. 19-24.
7. Billingsley, P. (1968). Convergence of Probability Measures. New York: Wiley.
8. Ethier, S. N., Kurtz, T. G. (1986). Markov Processes, Characterization and Convergence. New York: J. Wiley & Sons.
9. Korolyuk, V. S., Swishchuk, A. V. (1994). Random Evolutions. Kluwer Acad. Publ.
10. Neuts, M. (1989). Structured Stochastic Matrices of M/G/1 Type and their Applications. New York, Basel: Marcel Dekker.
11. Pinsky, M. (1975). Random Evolutions. Lecture Notes in Math. 451, New York: Springer, pp. 89-100.
12. Skorokhod, A. V. (1956). Limit theorems for random processes. Theory Probab. Appl. 1:289-319.
13. Skorokhod, A. V. (1989). Asymptotic Methods in the Theory of Stochastic Differential Equations. Providence, RI: Amer. Math. Soc.