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The talk will develop an infinitedimensional Hilbert manifold of probability measures. The manifold, M, retains the first and second order features of finitedimensional information geometry: the αdivergences admit first derivatives and mixed second derivatives, enabling the definition of the Fisher metric as a pseudoRiemannian metric. M was constructed with the FenchelLegendre transform between KullbackLeibler divergences, and its role in Bayesian estimation, in mind. This transform retains, on M, the symmetry of the finitedimensional case. Many of the manifolds of finitedimensional information geometry are shown to be C∞embedded submanifolds of M. The recursive equations of nonlinear filtering are usually expressed in terms of the Ito stochastic calculus, in which the socalled L2 theory is particularly simple and elegant. The Hilbert nature of M lends itself to this theory. By expressing the equations of nonlinear filtering for Markov processes in terms of stochastic processes on M, we show that the quadratic variation of a filter, in the Fisher metric, bears a simple relation to its rate of information supply. The filter representation can also be used as a basis for projective approximations of the type proposed by Brigo, Hanzon and Le Gland. Host: Frank Alexander, 6654518, Institutes Office 