BURA Collection:
http://bura.brunel.ac.uk/handle/2438/235
2014-04-20T14:05:10Z
2014-04-20T14:05:10Z
Signal processing with Lévy information
Brody, DC
Hughston, LP
Yang, X
http://bura.brunel.ac.uk/handle/2438/8213
2014-03-27T10:50:44Z
2013-01-01T00:00:00Z
Title: Signal processing with Lévy information
Authors: Brody, DC; Hughston, LP; Yang, X
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.
2013-01-01T00:00:00Z
General theory of geometric Lévy models for dynamic asset pricing
Brody, DC
Hughston, LP
Mackie, E
http://bura.brunel.ac.uk/handle/2438/8211
2014-03-27T10:39:17Z
2012-01-01T00:00:00Z
Title: General theory of geometric Lévy models for dynamic asset pricing
Authors: Brody, DC; Hughston, LP; Mackie, E
Abstract: The geometric Lévy model (GLM) is a natural generalization of the geometric Brownian motion (GBM) model used in the derivation of the Black–Scholes formula. The theory of such models simplifies considerably if one takes a pricing kernel approach. In one dimension, once the underlying Lévy process has been specified, the GLM has four parameters: the initial price, the interest rate, the volatility and the risk aversion. The pricing kernel is the product of a discount factor and a risk aversion martingale. For GBM, the risk aversion parameter is the market price of risk. For a GLM, this interpretation is not valid: the excess rate of return is a nonlinear function of the volatility and the risk aversion. It is shown that for positive volatility and risk aversion, the excess rate of return above the interest rate is positive, and is increasing with respect to these variables. In the case of foreign exchange, Siegel's paradox implies that one can construct foreign exchange models for which the excess rate of return is positive for both the exchange rate and the inverse exchange rate. This condition is shown to hold for any geometric Lévy model for foreign exchange in which volatility exceeds risk aversion.
Description: Copyright © 2012 The Royal Society. This is the author's final version of the article. The final publication is available from the link below.
2012-01-01T00:00:00Z
Dequantization of the Dirac monopole
Brody, DC
http://bura.brunel.ac.uk/handle/2438/8210
2014-03-27T10:32:59Z
2009-01-01T00:00:00Z
Title: Dequantization of the Dirac monopole
Authors: Brody, DC
Abstract: Using a sheaf-theoretic extension of conventional principal bundle theory, the Dirac monopole is formulated as a spherically symmetric model free of singularities outside the origin such that the charge may assume arbitrary real values. For integral charges, the construction effectively coincides with the usual model. Spin structures and Dirac operators are also generalized by the same technique.
Description: Copyright © 2009 The Royal Society. This is the author's final version of the article. The final publication is available from the link below.
2009-01-01T00:00:00Z
Path finding methods accounting for stoichiometry in metabolic networks
Pey, J
Prada, J
Beasley, JE
Planes, FJ
http://bura.brunel.ac.uk/handle/2438/8156
2014-03-24T10:28:57Z
2011-01-01T00:00:00Z
Title: Path finding methods accounting for stoichiometry in metabolic networks
Authors: Pey, J; Prada, J; Beasley, JE; Planes, FJ
Abstract: Graph-based methods have been widely used for the analysis of biological networks. Their application to metabolic networks has been much discussed, in particular noting that an important weakness in such methods is that reaction stoichiometry is neglected. In this study, we show that reaction stoichiometry can be incorporated into path-finding approaches via mixed-integer linear programming. This major advance at the modeling level results in improved prediction of topological and functional properties in metabolic networks.
Description: Copyright © 2011 Pey et al.; licensee BioMed Central Ltd. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
2011-01-01T00:00:00Z