Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-24T13:22:38.500Z Has data issue: false hasContentIssue false
  • English
  • Français

INTEGRAL EQUATION METHODS IN CHANGE-POINT DETECTION PROBLEMS

Part of: Stochastic processes

Published online by Cambridge University Press:  28 February 2012

GABRIEL MITITELU
GABRIEL MITITELU*
Affiliation:
Department of Mathematical Sciences, University of Technology, Sydney, PO Box 123, Broadway, NSW 2007, Australia (email: [email protected])
Rights & Permissions [Opens in a new window]

Abstract

An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'

Keywords

sequential analysiscontrol chartsEWMACUSUMintegral equations

MSC classification

Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory
Type
Abstracts of Australasian PhD Theses
Information
Bulletin of the Australian Mathematical Society , Volume 85 , Issue 3 , June 2012 , pp. 518 - 520
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

References

[1]Basseville, M. and Nikiforov, I. V., Detection of Abrupt Changes: Theory and Applications (Prentice Hall, Englewood Cliffs, NJ, 1993).Google Scholar
[2]Brodsky, B. E. and Darkhovsky, B. S., Nonparametric Change-Point Problems (Kluwer Academic, Dordrecht, 1993).Google Scholar
[3]Dufresne, D., ‘Fitting combinations of exponentials to probability distributions’, Appl. Stoch. Models Bus. Ind. 23 (2006), 23–48.CrossRefGoogle Scholar
[4]Feldmann, A. and Whitt, W., ‘Fitting mixtures of exponentials to long-tail distributions to analyze network performance models’, Performance Evaluation 31 (1998), 245–279.Google Scholar
[5]Jacobsen, M. and Jensen, T., ‘Exit time for a class of piecewise exponential Markov processes with two-sided jumps’, Technical Report, Department of Applied Mathematics and Statistics, University of Copenhagen, 2007.CrossRefGoogle Scholar
[6]Larralde, L., ‘A first passage time distribution for a discrete version of the Ornstein–Uhlenbeck process’, J. Phys. A: Math. General 37 (2004), 3759–3767.CrossRefGoogle Scholar
[7]Mititelu, G., Areepong, Y., Sukparungsee, S. and Novikov, A. A., ‘Some analytical results on CUSUM and EWMA control charts’, Proc. Int. Conf. in Mathematics and Applications (ICMA-MU 2009), Bangkok, Thailand, 2009.Google Scholar
[8]Mititelu, G., Areepong, Y., Sukparungsee, S. and Novikov, A. A., ‘Explicit analytical solutions for the average run length of CUSUM and EWMA charts’, East–West J. Math., special volume, 2010, Contributions in Mathematics and Applications III (2010), pp. 253–265.Google Scholar
[9]Mititelu, G., Mazalov, V. and Novikov, A. A., ‘On CUSUM procedure for hyperexponential distribution’, Stat. Probab. Lett., in press.Google Scholar
[10]Moustakides, G. V., Polunchenko, A. S. and Tartakovsky, A. G., ‘A numerical approach to performance analysis of quickest change-point detection procedures’, Statist. Sinica 21(2) (2009), 571–596.Google Scholar