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A poisson process whose rate is a hidden Markov process

Published online by Cambridge University Press:  01 July 2016

D. S. Freed  and
L. A. Shepp
D. S. Freed
Affiliation:
Harvard University
L. A. Shepp*
Affiliation:
Bell Laboratories
*
∗∗Postal address: Bell Laboratories, 600 Mountain Ave, Murray Hill, NJ 07924, U.S.A.
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Abstract

Let a Poisson process be observed whose output rate is one of two levels given by the state of an unseen Markov process. If one of the levels is 0, a simple formula is given for the best guess of the state at any instant based on the stream of past Poisson events. In other cases bounds are given for the likelihood ratio of the state probabilities given the event stream.

Keywords

POISSONCOXDOUBLY STOCHASTICHIDDEN RATELIKELIHOOD RATIO
Type
Research Article
Information
Advances in Applied Probability , Volume 14 , Issue 1 , March 1982 , pp. 21 - 36
Copyright
Copyright © Applied Probability Trust 1982 

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Footnotes

a

Present address: 970 Evans Hall, Mathematics Department, University of California, Berkeley, CA 94720, U.S.A.

Research carried out while this author was a summer employee at Bell Laboratories.

References

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