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We consider estimation problems, in which the estimand, X, and observation, Y , take values in measurable spaces. Regular conditional versions of the forward and inverse Bayes formula are shown to have dual variational characterisations involving the minimisation of an apparent information, and the maximisation of a compatible information. These both have… (More)

We investigate the information theoretic properties of Kalman–Bucy filters in continuous time, developing notions of information supply, storage and dissipa-tion. Introducing a concept of energy, we develop a physical analogy in which the unobserved signal describes a statistical mechanical system interacting with a heat bath. The abstract 'universe'… (More)

We investigate the information theoretic properties of Kalman-Bucy filters in continuous time, developing notions of information supply, storage and dissipation. Introducing a concept of energy, we develop a physical analogy in which the unobserved signal describes a statistical mechanical system interacting with a heat bath. The abstract 'universe'… (More)

This paper is dedicated by Sanjoy Mitter to Alain Bensoussan as a token of his friendship and intellectual collaboration over many years.

We investigate the information theoretic properties of Kalman-Bucy filters in continuous time, developing notions of information supply, storage and dissipation. By introducing a concept of energy, we develop a physical analogy in which the unobservable signal describes a statistical mechanical system interacting with a heat bath. The abstract 'universe'… (More)

We determine the maximum amount of work extractable in finite time by a demon performing continuous measurements on a quadratic Hamiltonian system subjected to thermal fluctuations, in terms of the information extracted from the system. The maximum work demon is found to apply a high-gain continuous feedback involving a Kalman-Bucy estimate of the system… (More)