Probabilistic methods in problems of applied analysis (Q1893928)

The author gives some examples of the applications of probabilistic methods in different areas of analysis. They are: the application of the law of large numbers in the approximation theory; the use of the infinite divisibility for refutation of Robertson's conjecture and for the deconvolution of the positive function; the application of Poisson processes and the central limit theorem to a problem concerning the breakdown of insulator gases by ionization (this issue is considered especially minutely).