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Title: Signal processing with Lévy information
Authors: Brody, DC
Hughston, LP
Yang, X
Keywords: Signal processing;Lévy process;Esscher transformation;Nonlinear filtering;Information process;Cybernetics
Issue Date: 2013
Publisher: The Royal Society
Citation: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 469(2149), Article 20120433, 2013
Abstract: Lévy processes, which have stationary independent increments, are ideal for modelling the various types of noise that can arise in communication channels. If a Lévy process admits exponential moments, then there exists a parametric family of measure changes called Esscher transformations. If the parameter is replaced with an independent random variable, the true value of which represents a ‘message’, then under the transformed measure the original Lévy process takes on the character of an ‘information process’. In this paper we develop a theory of such Lévy information processes. The underlying Lévy process, which we call the fiducial process, represents the ‘noise type’. Each such noise type is capable of carrying a message of a certain specification. A number of examples are worked out in detail, including information processes of the Brownian, Poisson, gamma, variance gamma, negative binomial, inverse Gaussian and normal inverse Gaussian type. Although in general there is no additive decomposition of information into signal and noise, one is led nevertheless for each noise type to a well-defined scheme for signal detection and enhancement relevant to a variety of practical situations.
Description: Copyright @ 2012 The Author(s) Published by the Royal Society. This is the author's final version of the article. The final publication is available from the link below.
ISSN: 1364-5021
Appears in Collections:Publications
Dept of Mathematics Research Papers
Mathematical Sciences

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