Open Access
2009 Nonlinear filtering with signal dependent observation noise
Dan Crisan, Michael Kouritzin, Jie Xiong
Author Affiliations +
Electron. J. Probab. 14: 1863-1883 (2009). DOI: 10.1214/EJP.v14-687


The paper studies the filtering problem for a non-classical frame- work: we assume that the observation equation is driven by a signal dependent noise. We show that the support of the conditional distri- bution of the signal is on the corresponding level set of the derivative of the quadratic variation process. Depending on the intrinsic dimension of the noise, we distinguish two cases: In the first case, the conditional distribution has discrete support and we deduce an explicit represen- tation for the conditional distribution. In the second case, the filtering problem is equivalent to a classical one defined on a manifold and we deduce the evolution equation of the conditional distribution. The re- sults are applied to the filtering problem where the observation noise is an Ornstein-Uhlenbeck process.


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Dan Crisan. Michael Kouritzin. Jie Xiong. "Nonlinear filtering with signal dependent observation noise." Electron. J. Probab. 14 1863 - 1883, 2009.


Accepted: 2 September 2009; Published: 2009
First available in Project Euclid: 1 June 2016

zbMATH: 1191.60050
MathSciNet: MR2540851
Digital Object Identifier: 10.1214/EJP.v14-687

Primary: 60G35
Secondary: 60G30

Keywords: Nonlinear filtering , Ornstein Uhlenbeck Noise , Signal-

Vol.14 • 2009
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