901 research outputs found
On mutual information, likelihood-ratios and estimation error for the additive Gaussian channel
This paper considers the model of an arbitrary distributed signal x observed
through an added independent white Gaussian noise w, y=x+w. New relations
between the minimal mean square error of the non-causal estimator and the
likelihood ratio between y and \omega are derived. This is followed by an
extended version of a recently derived relation between the mutual information
I(x;y) and the minimal mean square error. These results are applied to derive
infinite dimensional versions of the Fisher information and the de Bruijn
identity. The derivation of the results is based on the Malliavin calculus.Comment: 21 pages, to appear in the IEEE Transactions on Information Theor
Rotations and Tangent Processes on Wiener Space
The paper considers (a) Representations of measure preserving transformations
(``rotations'') on Wiener space, and (b) The stochastic calculus of variations
induced by parameterized rotations \{T_\theta w, 0 \le \theta \le \eps\}:
``Directional derivatives'' , ``vector
fields'' or ``tangent processes'' and flows
of rotations.Comment: 29 page
- …