Moments of claims in a Markovian environment

This paper considers discounted aggregate claims when the claim rates and sizes fluctuate according to the state of the risk business. We provide a system of differential equations for the Laplace–Stieltjes transform of the distribution of discounted aggregate claims under this assumption. Using the differential equations, we present the first two moments of discounted aggregate claims in a Markovian environment. We also derive simple expressions for the moments of discounted aggregate claims when the Markovian environment has two states. Numerical examples are illustrated when the claim sizes are specified.     

Recurrent solar wind streams

A new approach to investigating the statistical relationship between certain solar features and recurrent wind streams is presented. This approach is based, on a comparative analysis of the distributions of lifetimes of a set of solar features, recurrent geomagnetic disturbances, and geomagnetic “calms.” Correlation coefficients of 0.81, 0.85, 0.79, and 0.77 are found for the distributions of several solar features—filaments, large-scale magnetic fields, coronal features, and coronal holes, respectively—and recurrent geomagnetic disturbances. A correlation factor of 0.97 between the distributions of geomagnetic “calms” and active regions is found. The combined evidence indicates that no specific type of solar feature is responsible for the recurrent stream activity. Rather, the configuration of the large-scale magnetic field of the Sun appears to control the permanently existing corpuscular activity. Since prominences trace polarity division lines of the large-scale magnetic field structure of the Sun, they have been checked as a possible general predictor of recurrent corpuscular activity; their parameters could present the most reliable indices that relate closely with trends in geomagnetic disturbances. A comparative analysis of cyclic variations of sunspot numbers, the total number of prominences, the relative number of low-height (<-20″) prominences, and recurrent geomagnetic storms is made for solar cycle N16. The relative number of low-height prominences is found to correlate broadly (0.83) with recurrent wind streams. P. K. Shternberg State Astronomical Institute, Moscow, Russia; National Solar Observatory, Sacramento Peak, U.S. Published in Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 2, pp. 145–151, February, 1998.