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September 2015 The Kalman-Bucy filter for integrable Lévy processes with infinite second moment
David Applebaum, Stefan Blackwood
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J. Appl. Probab. 52(3): 636-648 (September 2015). DOI: 10.1239/jap/1445543837

Abstract

We extend the Kalman-Bucy filter to the case where both the system and observation processes are driven by finite dimensional Lévy processes, but whereas the process driving the system dynamics is square-integrable, that driving the observations is not; however it remains integrable. The main result is that the components of the observation noise that have infinite variance make no contribution to the filtering equations. The key technique used is approximation by processes having bounded jumps.

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David Applebaum. Stefan Blackwood. "The Kalman-Bucy filter for integrable Lévy processes with infinite second moment." J. Appl. Probab. 52 (3) 636 - 648, September 2015. https://doi.org/10.1239/jap/1445543837

Information

Published: September 2015
First available in Project Euclid: 22 October 2015

MathSciNet: MR3414982
zbMATH: 1326.60051
Digital Object Identifier: 10.1239/jap/1445543837

Subjects:
Primary: 60G51
Secondary: 60G35 , 60H10 , 62M20 , 93E11

Keywords: Kalman-Bucy filter , Lévy process , Riccati equation

Rights: Copyright © 2015 Applied Probability Trust

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Vol.52 • No. 3 • September 2015
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