Geodesic
To the invariance principle
Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 2, pp. 239-261

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Five functionals of the sums of independent random variables are discussed. The asymptotic analysis of these functionals played an important role in the development of the invariance principle. It is demonstrated that the weak convergence of each of these appropriately generalized functionals is equivalent to the applicability of the central limit theorem to sums of random variables on the basis of which the functionals are constructed.
Keywords: independent random variables, random broken line, process of Brownian motion, limit theorems for functionals of random variables. 
@article{TVP_1997_42_2_a1,
     author = {V. M. Kruglov},
     title = {To the invariance principle},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {239--261},
     publisher = {mathdoc},
     volume = {42},
     number = {2},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1997_42_2_a1/}
}
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V. M. Kruglov. To the invariance principle. Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 2, pp. 239-261. http://geodesic.mathdoc.fr/item/TVP_1997_42_2_a1/