@article{EJP687,
author = {Dan Crisan and Michael Kouritzin and Jie Xiong},
title = {Nonlinear filtering with signal dependent observation noise},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {14},
year = {2009},
keywords = {Nonlinear Filtering, Ornstein Uhlenbeck Noise, Signal-},
abstract = {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.},
pages = {no. 63, 1863-1883},
issn = {1083-6489},
doi = {10.1214/EJP.v14-687},
url = {http://ejp.ejpecp.org/article/view/687}}