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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.

MSC:

60F17 Functional limit theorems; invariance principles
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