Exponential martingales and changes of measure for counting processes

We give sufficient criteria for the Dol\'eans-Dade exponential of a stochastic integral with respect to a counting process local martingale to be a true martingale. The criteria are adapted particularly to the case of counting processes and are sufficiently weak to be useful and verifiable, as we illustrate by several examples. In particular, the criteria allow for the construction of for example nonexplosive Hawkes processes as well as counting processes with stochastic intensities depending on diffusion processes

The red-sky enigma over Svalbard in December 2002

On 6 December 2002, during winter darkness, an extraordinary event occurred in the sky, as viewed from Longyearbyen (78° N, 15° E), Svalbard, Norway. At 07:30 UT the southeast sky was surprisingly lit up in a deep red colour. The light increased in intensity and spread out across the sky, and at 10:00 UT the illumination was observed to reach the zenith. The event died out at about 12:30 UT. Spectral measurements from the Auroral Station in Adventdalen confirm that the light was scattered sunlight. Even though the Sun was between 11.8 and 14.6deg below the horizon during the event, the measured intensities of scattered light on the southern horizon from the scanning photometers coincided with the rise and setting of the Sun. Calculations of actual heights, including refraction and atmospheric screening, indicate that the event most likely was scattered solar light from a target below the horizon. This is also confirmed by the OSIRIS instrument on board the Odin satellite. The deduced height profile indicates that the scattering target is located 18–23km up in the stratosphere at a latitude close to 73–75° N, southeast of Longyearbyen. The temperatures in this region were found to be low enough for Polar Stratospheric Clouds (PSC) to be formed. The target was also identified as PSC by the LIDAR systems at the Koldewey Station in Ny-Ålesund (79° N, 12° E). The event was most likely caused by solar illuminated type II Polar Stratospheric Clouds that scattered light towards Svalbard. Two types of scenarios are presented to explain how light is scattered.publishedVersio

Aerosol chemical composition and distribution during the Pacific Exploratory Mission (PEM) Tropics

Distributions of aerosol-associated soluble ions over much of the South Pacific were determined by sampling from the NASA DC-8 as part of the Pacific Exploratory Mission (PEM) Tropics campaign. The mixing ratios of all ionic species were surprisingly low throughout the free troposphere (2-12 km), despite the pervasive influence from biomass burning plumes advecting over the South Pacific from the west during PEM-Tropics. At the same time, the specific activity of 7Be frequently exceeded 1000 fCi m-3 through much of the depth of the troposphere. These distributions indicate that the plumes must have been efficiently scavenged by precipitation (removing the soluble ions), but that the scavenging must have occurred far upwind of the DC-8 sampling regions (otherwise 7Be activities would also have been low). This inference is supported by large enhancements of HNO3 and carboxylic acids in many of the plumes, as these soluble acidic gases would also be readily scavenged in any precipitation events. Decreasing mixing ratios of NH4 + with altitude in all South Pacific regions sampled provide support for recent suggestions that oceanic emissions of NH3 constitute a significant source far from continents. Our sampling below 2 km reaffirms the latitudinal pattern in the methylsulfonate/non-sea-salt sulfate (MSA/nss SO4 =) molar ratio established through surface-based and shipboard sampling, with values increasing from \u3c0.05 in the tropics to nearly 0.6 at 70°S. However, we also found very high values of this ratio (0.2-0.5) at 10 km altitude above the intertropical convergence zone near 10°N. It appears that wet convective pumping of dimethylsulfide from the tropical marine boundary layer is responsible for the high values of the MSA/nss SO4 = ratio in the tropical upper troposphere. This finding complicates use of this ratio to infer the zonal origin of biogenic S transported long distances. Copyright 1999 by the American Geophysical Union

Explicit formulae in probability and in statistical physics

We consider two aspects of Marc Yor's work that have had an impact in statistical physics: firstly, his results on the windings of planar Brownian motion and their implications for the study of polymers; secondly, his theory of exponential functionals of Levy processes and its connections with disordered systems. Particular emphasis is placed on techniques leading to explicit calculations.Comment: 14 pages, 2 figures. To appear in Seminaire de Probabilites, Special Issue Marc Yo

Study of the bivariate survival data using frailty models based on Lévy processes

Frailty models allow us to take into account the non-observable inhomogeneity of individual hazard functions. Although models with time-independent frailty have been intensively studied over the last decades and a wide range of applications in survival analysis have been found, the studies based on the models with time-dependent frailty are relatively rare. In this paper, we formulate and prove two propositions related to the identifiability of the bivariate survival models with frailty given by a nonnegative bivariate Lévy process. We discuss parametric and semiparametric procedures for estimating unknown parameters and baseline hazard functions. Numerical experiments with simulated and real data illustrate these procedures. The statements of the propositions can be easily extended to the multivariate case

Postoperative inflammation and insulin resistance in relation to body composition, adiposity and carbohydrate treatment: a randomised controlled study

Background and Aims: The aims of this study were to identify whether differences in distribution of adipose tissue and skeletal muscle in obese and non-obese individuals contribute to the magnitude of the postoperative inflammatory response and insulin resistance, with and without preoperative treatment with carbohydrate drinks. Methods: Thirty-two adults (16 obese/16 non-obese) undergoing elective major open abdominal surgery participated in this 22 factorial, randomised, double-blind, placebo-controlled study. Participants received Nutricia preOp® or placebo (800 ml on the night before surgery/400 ml 2-3 h preoperatively) after stratifying for obesity. Insulin sensitivity was measured using the hyperinsulinaemic-euglycaemic clamp pre- and postoperatively. Vastus lateralis, omental and subcutaneous fat biopsies were taken pre- and postoperatively and analysed after RNA extraction. The primary endpoint was within subject differences in insulin sensitivity. Results: Major abdominal surgery was associated with a 42% reduction in insulin sensitivity from mean(SD) M value of 37.3(11.8) μmol kg-1 fat free mass (FFM) to 21.7(7.4) μmol kg-1 67 FFM, but this was not influenced by obesity or preoperative carbohydrate treatment. Activation of the triggering receptor expressed on myeloid cells (TREM1) pathway was seen in response to surgery in omental fat samples. In postoperative muscle samples, gene expression differences indicated activation of the peroxisome proliferator-activated receptor (PPAR-α)/retinoid X-receptor (RXR-α) pathway in obese but not in non-obese participants. There were no significant changes in gene expression pathways associated with carbohydrate treatment. Conclusion: The reduction in insulin sensitivity associated with major abdominal surgery was confirmed but there were no differences associated with preoperative carbohydrates or obesity

Intra-Domain Delay-Based Quality of Service Using Differentiated Routing

Differentiated routing is an approach to providing service differentiation in networks, a field that is currently receiving significant research attention. In this report we present an algorithm, namely Intra-Domain Differentiated Routing (IDDR), which supports qualitative delay differentiation in IP networks. We review existing differentiated routing approaches and then introduce IDDR and present initial results. We demonstrate that using IDDR we can achieve qualitative delay differentiation for two classes of flows