Filtering a Markov-modulated random measure

Robert J. Elliott, Tak Kuen Siu, Hailiang Yang

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)
8 Downloads (Pure)


We develop a new exact filter when a hidden Markov chain influences both the sizes and times of a marked point process. An example would be an insurance claims process, where we assume that both the stochastic intensity of the claim arrivals and the distribution of the claim sizes depend on the states of an economy. We also develop the robust filter-based and smoother-based EM algorithms for the on-line recursive estimates of the unknown parameters in the Markov-modulated random measure. Our development is in the framework of modern theory of stochastic processes.

Original languageEnglish
Article number5340543
Pages (from-to)74-88
Number of pages15
JournalIEEE Transactions on Automatic Control
Issue number1
Publication statusPublished - Jan 2010

Bibliographical note

Copyright 2010 IEEE. Reprinted from IEEE Transactions on automatic control, Vol.55, No.1, pp.74-88. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Macquarie University’s products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to By choosing to view this document, you agree to all provisions of the copyright laws protecting it.


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