Electronic Communications in Probability

Nonlinear filtering with degenerate noise

David Jaures Fotsa–Mbogne and Etienne Pardoux

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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

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

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

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Zentralblatt MATH identifier

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

nonlinear filtering singular observation noise

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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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