ISSN 0021-3454 (print version)
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10
Issue
vol 60 / OCTOBER, 2017
Article

DOI 10.17586/0021-3454-2017-60-8-721-727

UDC 517.14

APPLICATION OF ALFREY'S FORMULA IN THE THEORY OF RANDOM PROCESSES

V. A. Smagin
A. F. Mozhaysky Military Space Academy, Department of Metrological Maitenance, St. Petersburg; Professor


I. A. Karabelnikov
A. F. Mozhaisky Military Space Academy, Military Institute; Head of Department


I. S. Petrova
A. F. Mozhaisky Military Space Academy, Military Institute; Researcher


Abstract. An approximate method using Alfrey’s formula is proposed for derivation of digital values of function with image represented by a complex Laplace transform. The formula was obtained in the study of mechanical properties of high polymers; it is based on filtering the integrand of Laplace transform with the delta-function. A solution of an integral equations with temporal redundancy for the probability of task execution by a system is presented as an example. Attempts to improve the accuracy of the inverse transformation using the mathematical apparatus of Haar’s or Widder’s methods are reported to be unsuccessful.
Keywords: Laplace transform, inverse transformation, Alfrey’s formula, integral equations with temporal redundancy, probability of task execution, method of moments, information task

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