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We investigate the information theoretic properties of KalmanBucy 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)

- Sanjoy K. Mitter, Nigel J. Newton
- SIAM J. Control and Optimization
- 2003

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)

- Nigel J. Newton
- SIAM Journal of Applied Mathematics
- 1994

This article develops some variance reduction techniques for the Monte-Carlo integration of functionals of the solutions of It6 stochastic differential equations (sdes). The Monte-Carlo method for sdes offers a means of calculating solutions to certain types of parabolic partial differential equation and so has applications in various fields including… (More)

- Nigel J. Newton
- SIAM J. Control and Optimization
- 2007

- Nigel J. Newton
- SIAM J. Control and Optimization
- 2006

We investigate the information theoretic properties of KalmanBucy 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)

- Nigel J. Newton
- Monte Carlo Meth. and Appl.
- 2001

- Henrik Sandberg, Jean-Charles Delvenne, Nigel J Newton, Sanjoy K Mitter
- Physical review. E, Statistical, nonlinear, and…
- 2014

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)

In his book, Filtrage Optimal des Systémes Linéaires, Alain Bensoussan presented a variational view of optimal filtering for linear infinite-dimensional stochastic differential systems. The viewpoint he presented is related to the work of Bryson and Frazier [1] where the Kalman Filter was viewed in terms of the solution of a linear optimal control problem… (More)

- Nigel J. Newton
- 2000

A Bayesian estimation problem is considered, in which the observation is a vector-valued, continuous-time stochastic process of the ‘signal-plus-white-noise’ variety and approximations based on sampling and quantisation of this process are developed. The problem includes continuous-time nonlinear lters, interpolators and extrapolators as special cases. The… (More)