Likhoded, N. A.; Sobolevskij, P. I. On some approach to the construction of cubature formulae with prescribed summarized degree of accuracy for multiple probability integrals. (Russian. English summary) Zbl 0589.65023 Dokl. Akad. Nauk BSSR 28, 773-776 (1984). Cubature formulae for multiple integrals with densities corresponding to infinitely divisible distributions are obtained by projecting formulae of a prescribed degree of accuracy for approximate calculation of continuous integrals on measures generated by homogeneous processes with independent increments. These cubature formulae are recurrent, they have prescribed summarized degree of accuracy and they converge - as the dimension tends to infinity - to the approximate formulae for continuous integrals. Reviewer: E.Rozmarová MSC: 65D32 Numerical quadrature and cubature formulas 41A55 Approximate quadratures 65D20 Computation of special functions and constants, construction of tables 33B20 Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) 41A63 Multidimensional problems 60H05 Stochastic integrals 65C99 Probabilistic methods, stochastic differential equations Keywords:multiple probability integrals; infinitely divisible distributions; convergence; Cubature formulae PDFBibTeX XMLCite \textit{N. A. Likhoded} and \textit{P. I. Sobolevskij}, Dokl. Akad. Nauk BSSR 28, 773--776 (1984; Zbl 0589.65023)