On the Innovations Conjecture of Nonlinear Filtering with Dependent Data
Andrew Heunis, University of Waterloo
Vladimir Lucic, Barclays Capital
Abstract
We establish the innovations conjecture
for a nonlinear filtering problem
in which the signal to be estimated is conditioned
by the observations.
The approach uses only elementary stochastic analysis,
together with a variant due to J.M.C. Clark of
a theorem of Yamada and Watanabe on pathwise-uniqueness
and strong solutions of stochastic differential
equations.
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