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On some finite dimensional nonlinear filters for certain diffusions observed in correlated noise
Authors:Ofer Zeitouni
Affiliation:1. Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy;2. Dipartimento di Matematica, Università di Pisa, Largo Pontecorvo 5, I-56127, Pisa, Italy;1. Inorganic Membranes, MESA+ Institute for Nanotechnology, University of Twente, 7500 AE, Enschede, the Netherlands;2. Sustainable Polymer Chemistry, Department of Molecules & Materials, MESA+ Institute for Nanotechnology, University of Twente, 7500 AE, Enschede, the Netherlands;3. Institut Européen des Membranes, Univ Montpellier, CNRS-UM-ENSCM, Place Eugène Bataillon, 34095, Montpellier, Cedex 5, France;1. Bank of America, One Bryant Park, New York, NY, 10036, USA;2. Morgan Stanley, 1585 Broadway, New York, NY, 10036, USA;1. Dept. of Mathematics, University of Houston, Houston, TX 77204, United States of America;2. Dept. of Mathematics, Ruhr University Bochum, 44780 Bochum, Germany;3. IMPA, Estrada Dona Castorina 110, Rio de Janeiro, Brazil
Abstract:An extension of the one dimensional Bene nonlinear filter to the case of correlated process and observation noises is presented. Conditions are derived so that the optimal nonlinear filter is finite dimensional.
Keywords:Nonlinear filtering   Finite dimensional filters
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