Uniqueness of the Embedding Continuous Convolution Semigroup of a Gaussian Probability Measure on the Affine Group and an Application in Mathematical Finance

Let {μ(i)t}t≥0 ( i=1,2 ) be continuous convolution semigroups (c.c.s.) of probability measures on Aff(1) (the affine group on the real line). Suppose that μ(1)1=μ(2)1 . Assume furthermore that {μ(1)t}t≥0 is a Gaussian c.c.s. (in the sense that its generating distribution is a sum of a primitive distribution and a second-order differential operator). Then μ(1)t=μ(2)t for all t≥0 . We end up with a possible application in mathematical finance.

The role of chance events in the school-to-work transition: The influence of demographic, personality and career development variables

Chance events are considered important in career development, yet little empirical research is available on their predictors and consequences. The present study investigated socio-demographic (gender, nationality, school-type), personality (openness, locus of control) and career development variables (career decidedness, career planning) in relation to perceived chance events with a retrospective (N = 229, eleventh grade), and 1-year longitudinal prospective study (N = 245, eighth/ninth grade) among Swiss adolescents. The results showed that the majority of both groups reported a significant influence of chance events on their transition from compulsory school to vocational education or high school. Importance of chance events related to socio-demographics and personality but not career preparation. Career preparation and chance events predicted subjective career success in terms of wish correspondence and overall satisfaction with transition outcome among the younger cohort. Implications include the necessity to integrate both thorough career preparation and chance events in theory and counseling practice.

Signal Processing for the Measurement of the Deuterium/Hydrogen Ratio in the Local Interstellar Medium

We report on a comprehensive signal processing procedure for very low signal levels for the measurement of neutral deuterium in the local interstellar medium from a spacecraft in Earth orbit. The deuterium measurements were performed with the IBEX-Lo camera on NASA’s Interstellar Boundary Explorer (IBEX) satellite. Our analysis technique for these data consists of creating a mass relation in three-dimensional time of flight space to accurately determine the position of the predicted D events, to precisely model the tail of the H events in the region where the H tail events are near the expected D events, and then to separate the H tail from the observations to extract the very faint D signal. This interstellar D signal, which is expected to be a few counts per year, is extracted from a strong terrestrial background signal, consisting of sputter products from the sensor’s conversion surface. As reference we accurately measure the terrestrial D/H ratio in these sputtered products and then discriminate this terrestrial background source. During the three years of the mission time when the deuterium signal was visible to IBEX, the observation geometry and orbit allowed for a total observation time of 115.3 days. Because of the spinning of the spacecraft and the stepping through eight energy channels the actual observing time of the interstellar wind was only 1.44 days. With the optimised data analysis we found three counts that could be attributed to interstellar deuterium. These results update our earlier work.