@article{5fb780d4ea2a41499b5b7f32d50ef787,
title = "A problem in stochastic averaging of nonlinear filters",
abstract = "We consider the stochastic averaging of a particular degenerate problem in nonlinear filtering. In particular, we consider a problem on the cylinder with fast angular diffusion and slow axial diffusion. The observation process depends only on the fast angle. We show that as the separation of scales (between fast and slow) grows, one can approximate the filter for the original problem by a much simpler one. Although our problem is similar to a number of others considered in the literature, the techniques required are different from the known ones.",
keywords = "Homogenization, Nonlinear filtering, Stochastic partial differential equations",
author = "Park, {Jun H.} and Namachchivaya, {N. Sri} and Sowers, {Richard B.}",
note = "Funding Information: The authors would like to acknowledge the support of AFOSR under grant No. FA9550-08-1-0206 and the National Science Foundation under grant Nos. CNS 05-40237, DMS 05-04581 and DMS 06-04249. Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the National Science Foundation. Part of the work was done while the authors were visiting the Mathematical Sciences Research Institute (MSRI). The authors gratefully acknowledge the hospitality of MSRI during its Spring 2007 program in Dynamical Systems. They would also like to acknowledge Professor Chris Jones of University of North Carolina, Chapel Hill for helpful discussions at the initial stage of this work during our stay at MSRI. Copyright: Copyright 2008 Elsevier B.V., All rights reserved.",
year = "2008",
doi = "10.1142/S0219493708002445",
language = "English (US)",
volume = "8",
pages = "543--560",
journal = "Stochastics and Dynamics",
issn = "0219-4937",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "3",
}