Signal processing with Levy information

Levy processes, which have stationary independent increments, are ideal for modelling the various types of noise that can arise in communication channels. If a Levy 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 Levy process takes on the character of an "information process". In this paper we develop a theory of such Levy information processes. The underlying Levy 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.Comment: 27 pages. Version to appear in: Proc. R. Soc. London

Lévy Information and the Aggregation of Risk Aversion

When investors have heterogeneous attitudes towards risk, it is reasonable to assume that each investor has a pricing kernel, and that these individual pricing kernels are aggregated to form a market pricing kernel. The various investors are then buyers or sellers depending on how their individual pricing kernels compare with that of the market. In Brownian-based models, we can represent such heterogeneous attitudes by letting the market price of risk be a random variable, the distribution of which corresponds to the variability of attitude across the market. If the flow of market information is determined by the movements of prices, then neither the Brownian driver nor the market price of risk are directly visible: the filtration is generated by an ‘information process’ given by a combination of the two. We show that the market pricing kernel is then given by the harmonic mean of the individual pricing kernels associated with the various market participants. Remarkably, with an appropriate definition of Lévy information one draws the same conclusion in the case when asset prices can jump. As a consequence, we are led to a rather general scheme for the management of investments in heterogeneous markets subject to jump risk

Pulmonary edema measured by MRI correlates with late-phase response to allergen challenge

Purpose: Asthma is associated with reversible airway obstruction, leucocyte infiltration, airways hyperresponsiveness (AHR) and airways remodelling. Fluid accumulation causes pulmonary oedema contributing to airways obstruction. We examined the temporal relationship between the late asthmatic response (LAR) following allergen challenge of sensitised guinea-pigs and pulmonary oedema measured by magnetic resonance imaging (MRI). Materials and Methods: Ovalbumin (OVA) sensitised guinea-pigs received either a single OVA inhalation (acute) or nine OVA inhalations at 48 h intervals (chronic). Airways obstruction was measured as specific airways conductance (sGaw) by whole body plethysmography. AHR to inhaled histamine and bronchoalveolar lavage for leucocyte counts were measured 24 h after a single or the final chronic ovalbumin challenges. MRI was performed at intervals after OVA challenge and high intensity oedemic signals quantified. Results: Ovalbumin caused early bronchoconstriction, followed at 7 h by a LAR and at 24 h AHR and leucocyte influx. The bright intensity MRI oedema signal, peaking at 7 h, was significantly (P<0.05) greater after chronic (9.0±0.7x103 mm3) than acute OVA (7.6±0.2x103 mm3). Dexamethasone treatment before acute OVA abolished the AHR and LAR and significantly reduced eosinophils and the bright intensity MRI oedema from 9.1±1.0 to 6.4±0.3x103 mm3. Conclusion: We show a temporal relationship between oedema and the LAR and their parallel reduction, along with eosinophils and AHR, by dexamethasone. This suggests a close causative association between pulmonary oedema and impaired airways function