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November 2014 Optimal filtering and the dual process
Omiros Papaspiliopoulos, Matteo Ruggiero
Bernoulli 20(4): 1999-2019 (November 2014). DOI: 10.3150/13-BEJ548

Abstract

We link optimal filtering for hidden Markov models to the notion of duality for Markov processes. We show that when the signal is dual to a process that has two components, one deterministic and one a pure death process, and with respect to functions that define changes of measure conjugate to the emission density, the filtering distributions evolve in the family of finite mixtures of such measures and the filter can be computed at a cost that is polynomial in the number of observations. Special cases of our framework include the Kalman filter, and computable filters for the Cox–Ingersoll–Ross process and the one-dimensional Wright–Fisher process, which have been investigated before. The dual we obtain for the Cox–Ingersoll–Ross process appears to be new in the literature.

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Omiros Papaspiliopoulos. Matteo Ruggiero. "Optimal filtering and the dual process." Bernoulli 20 (4) 1999 - 2019, November 2014. https://doi.org/10.3150/13-BEJ548

Information

Published: November 2014
First available in Project Euclid: 19 September 2014

zbMATH: 1302.60071
MathSciNet: MR3263096
Digital Object Identifier: 10.3150/13-BEJ548

Rights: Copyright © 2014 Bernoulli Society for Mathematical Statistics and Probability

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Vol.20 • No. 4 • November 2014
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