E lect r o n i c J o u r n a l o f P r o b a b ility Vol.13 (2008), Paper no. 72, pages 2190–2216. Journal URL http://www.math.washington.edu/~ejpecp/ On the Innovations Conjecture of Nonlinear Filtering with Dependent Data ∗ Andrew J. Heunis Department of Electrical and Computer Engineering University of Waterloo Waterloo, Ontario N2L 3G1, Canada e-mail: heunis@kingcong.uwaterloo.ca Vladimir M. Lucic Barclays Capital 5 The North Colonnade, Canary Warf London E14 4BB, United Kingdom e-mail: vladimir.lucic@btopenworld.com 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. Key words: nonlinear filter, innovations conjecture, pathwise-uniqueness. AMS 2000 Subject Classification: Primary 60G35; Secondary: 60H10, 60G44, 60G57. Submitted to EJP on November 11, 2007, final version accepted November 5, 2008. ∗ Supported by NSERC of Canada 2190