Conditional Time Before Ruin of an Insurance Company

The statistical characteristics of conditional time before ruin of an insurance company, including the distribution function of conditional time and its moments are examined.     

The Almost Sure Limit Theorem for Sums of Random Vectors

We establish a sufficient condition for an almost sure limit theorem for sums of independent random vectors under minimal moment conditions and assumptions on normalizing sequences. We provide an example showing that our condition is close to the optimal one, as well as a related sufficient condition due to Berkes and Dehling. Bibliography: 5 titles.     

Distribution density of the norm of a stable vector

Let B be a Banach space,X be a stable B -valued random vector with exponentd(0,2), and P(·) be the distribution density of the norm of X. In this paper we study the question of the boundedness of P. In particular, we construct examples of a space B with a symmetric stable vector X with exponentd(1,2) with unbounded P and prove that if X is a nondegenerate strictly stable vector with exponentd(0,1), then P is bounded.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 158, pp. 105–114, 1987.The author is grateful to Yu. A. Davydov, V. I. Paulauskas, V. Yu. Bentkus, and D. Pap for stimulating discussions of the subject of this paper. When the paper was finished the author learned that similar results are found in [9].     

Occupation times of Gaussian stationary processes

One finds and one investigates a class of almost smooth stationary Gaussian processes whose trajectories have no local time.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 97, pp. 110–126, 1980.     

The formation of InSi surface phase

The study of thin indium films on Si(1 1 1) using LEED, AES and ELS techniques was carried out. The ELS data were interpreted by means of the bulk plasmons theory. The formation of InSi surface phase both at RT and as a result of annealing was shown.     

Small deviation probability via chaining

We obtain several extensions of Talagrand’s lower bound for the small deviation probability using metric entropy. For Gaussian processes, our investigations are focused on processes with sub-polynomial and, respectively, exponential behaviour of covering numbers. The corresponding results are also proved for non-Gaussian symmetric stable processes, both for the cases of critically small and critically large entropy. The results extensively use the classical chaining technique; at the same time they are meant to explore the limits of this method.     

Computation of the exact asymptotic behavior of certain Gaussian large deviations

The asymptotic behavior of the distribution function and the density of certain Gaussian large deviations is investigated.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 184, pp. 189–199, 1990.     

The potential approximation in the theory of conical flows

The use of potential theory to describe external flows at intermediate supersonic velocities makes it possible to construct very fast algorithms for calculating the flow even in the presence of subsonic regions [1, 2]. However, this approach involves errors associated with the neglect of the increase of entropy in the bow shock. The magnitude of these errors and their effect on the values of the various flow parameters are most easily estimated with reference to examples of conical flows. The shock-capturing projection-grid method [3] is used for integrating the conical potential equation. The results of calculating the flow past circular and elliptical cones, a triangular plate and a V-wing are compared with the corresponding solutions of the system of Euler equations. The region of applicability of the potential model is determined and it is shown that the satisfaction of the Hugoniot shock polar equation at the bow shock increases the error of the pressure calculations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 112–118, May–June, 1990.In conclusion the authors wish to thank V. V. Kovalenko for calculating the Euler equations and A. N. Kraiko for discussing the results.