Electronic Communications in Probability

Nonlinear filtering with degenerate noise

David Jaures Fotsa–Mbogne and Etienne Pardoux

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Abstract

This paper studies a new type of filtering problem, where the diffusion coefficient of the observation noise is strictly positive only in the interior of the bounded interval where observation takes its values. We derive a Zakai and a Kushner–Stratonovich equation, and prove uniqueness of the measure–valued solution of the Zakai equation.

Article information

Source
Electron. Commun. Probab., Volume 22 (2017), paper no. 44, 14 pp.

Dates
Received: 14 February 2017
Accepted: 17 July 2017
First available in Project Euclid: 15 August 2017

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1502762750

Digital Object Identifier
doi:10.1214/17-ECP74

Mathematical Reviews number (MathSciNet)
MR3693770

Zentralblatt MATH identifier
06797797

Subjects
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05] 60H15: Stochastic partial differential equations [See also 35R60]

Keywords
nonlinear filtering singular observation noise

Rights
Creative Commons Attribution 4.0 International License.

Citation

Fotsa–Mbogne, David Jaures; Pardoux, Etienne. Nonlinear filtering with degenerate noise. Electron. Commun. Probab. 22 (2017), paper no. 44, 14 pp. doi:10.1214/17-ECP74. https://projecteuclid.org/euclid.ecp/1502762750


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References

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