Dimensional reduction in nonlinear filtering: A homogenization approach

Details Dimensional reduction in nonlinear filtering: A homogenization approach Dimensional reduction in nonlinear filtering: A homogenization approach

2011-12-13

arxiv.org/abs/1112.2986v1

Mathematics

Probability

27 pages

Scientific paper

We propose a homogenized filter for multiscale signals, which allows to
reduce the dimension of the system. We prove that the nonlinear filter
converges to our homogenized filter. This is achieved by a suitable asymptotic
expansion of the dual of the Zakai equation, and by probabilistically
representing the correction terms with the help of BDSDEs.

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