Zinchenko, N. M. The Skorokhod representation and strong invariance principle. (English. Ukrainian original) Zbl 0990.60029 Theory Probab. Math. Stat. 63, 51-63 (2001); translation from Teor. Jmovirn. Mat. Stat. 63, 49-60 (2000). The author considers a class of limit theorems which is called “strong invariance principle”. The presented survey of results consists of generalizations of Skorokhod embedding for martingales; estimates for approximation error in strong invariance principle; strong invariance principle for differently distributed random variables, for sums of random vectors, and for multiple sums of random variables with multiple indexes; strong invariance principle for the random variables in the domain of attraction of a stable law. Applications of strong invariance principle in probability theory and mathematical statistics are discussed. Reviewer: A.D.Borisenko (Kyïv) Cited in 1 ReviewCited in 1 Document MSC: 60F17 Functional limit theorems; invariance principles Keywords:Skorokhod embedding; strong invariance principle; limit theorems; approximation error PDFBibTeX XMLCite \textit{N. M. Zinchenko}, Teor. Ĭmovirn. Mat. Stat. 63, 49--60 (2000; Zbl 0990.60029); translation from Teor. Jmovirn. Mat. Stat. 63, 49--60 (2000)