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Nonlinear Filtering for Jump Diffusion Observations

Part of: Stochastic systems and control Markov processes

Published online by Cambridge University Press:  04 January 2016

Claudia Ceci  and
Katia Colaneri
Claudia Ceci*
Affiliation:
University of Chieti-Pescara
Katia Colaneri*
Affiliation:
University of Chieti-Pescara
*
∗ Postal address: Department of Economics, University of Chieti-Pescara, Viale Pindaro 42, I-65127 Pescara, Italy.
∗ Postal address: Department of Economics, University of Chieti-Pescara, Viale Pindaro 42, I-65127 Pescara, Italy.
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Abstract

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We deal with the filtering problem of a general jump diffusion process, X, when the observation process, Y, is a correlated jump diffusion process having common jump times with X. In this setting, at any time t the σ-algebra provides all the available information about Xt, and the central goal is to characterize the filter, πt, which is the conditional distribution of Xt given observations . To this end, we prove that πt solves the Kushner-Stratonovich equation and, by applying the filtered martingale problem approach (see Kurtz and Ocone (1988)), that it is the unique weak solution to this equation. Under an additional hypothesis, we also provide a pathwise uniqueness result.

Keywords

Filteringjump diffusion process

MSC classification

Primary: 93E11: Filtering 60J75: Jump processes 60J60: Diffusion processes
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 44 , Issue 3 , September 2012 , pp. 678 - 701
Copyright
© Applied Probability Trust 

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