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Uniqueness for measure-valued equations of nonlinear filtering for stochastic dynamical systems with Lévy noise

Part of: Stochastic analysis Stochastic processes

Published online by Cambridge University Press:  26 July 2018

Huijie Qiao
Huijie Qiao*
Affiliation:
Southeast University
*
* Postal address: Department of Mathematics, Southeast University, Nanjing, Jiangsu 211189, China. Email address: hjqiaogean@seu.edu.cn
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Abstract

In the paper we study the Zakai and Kushner–Stratonovich equations of the nonlinear filtering problem for a non-Gaussian signal-observation system. Moreover, we prove that under some general assumption, the Zakai equation has pathwise uniqueness and uniqueness in joint law, and the Kushner–Stratonovich equation is unique in joint law.

Keywords

Zakai equationKushner–Stratonovich equationuniqueness in joint lawpathwise uniqueness

MSC classification

Primary: 60G35: Signal detection and filtering 60G51: Processes with independent increments; L'evy processes 60H10: Stochastic ordinary differential equations
Type
Original Article
Information
Advances in Applied Probability , Volume 50 , Issue 2 , June 2018 , pp. 396 - 413
Copyright
Copyright © Applied Probability Trust 2018 

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