Zinchenko, Nadiya M. Limit theorems for sums of independent random variables and stochastic processes. (English) Zbl 0938.60010 Theory Stoch. Process. 3(19), No. 3-4, 501-510 (1997). A brief historical survey of results by B. Gnedenko and his students on one- and multidimensional stable laws and their domains of attraction is presented. Further development of this theory is discussed. Contributions by A. Khinchin and by B. Gnedenko to the theory of random processes with independent increments are described. Reviewer: A.V.Swishchuk (Kyïv) MSC: 60-03 History of probability theory 60E07 Infinitely divisible distributions; stable distributions 60B12 Limit theorems for vector-valued random variables (infinite-dimensional case) 60G51 Processes with independent increments; Lévy processes 01A60 History of mathematics in the 20th century Keywords:weak convergence; stable distributions; domain of attraction; semi-stable law; operator-stable law; growth rate; law of the iterated logarithm PDFBibTeX XMLCite \textit{N. M. Zinchenko}, Theory Stoch. Process. 3(19), No. 3--4, 501--510 (1997; Zbl 0938.60010)