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September 2012 Nonlinear filtering for jump diffusion observations
Claudia Ceci, Katia Colaneri
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Adv. in Appl. Probab. 44(3): 678-701 (September 2012). DOI: 10.1239/aap/1346955260

Abstract

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 FYt 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 FYt. 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.

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Claudia Ceci. Katia Colaneri. "Nonlinear filtering for jump diffusion observations." Adv. in Appl. Probab. 44 (3) 678 - 701, September 2012. https://doi.org/10.1239/aap/1346955260

Information

Published: September 2012
First available in Project Euclid: 6 September 2012

zbMATH: 1251.93123
MathSciNet: MR3024605
Digital Object Identifier: 10.1239/aap/1346955260

Subjects:
Primary: 60J60, 60J75, 93E11

Rights: Copyright © 2012 Applied Probability Trust

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Vol.44 • No. 3 • September 2012
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