Geodesic
On Borovkov's estimate in the Invariance Principle
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1776-1784

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The first general estimate in the functional CLT (i.e. in the Invariance Principle) was obtained by A. Borovkov in 1973 in terms of the Lyapunov fractions of order not greater than three. Here we present explicit numerical bounds for the constants in Borovkov's estimate. In addition, we have found similar but more precise estimates in terms of truncated Lyapunov fractions.
Keywords: estimates in the Invariance Principle, Prokhorov distance, Lyapunov fraction, truncated Lyapunov fraction. 
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     author = {A. I. Sakhanenko},
     title = {On {Borovkov's} estimate in the {Invariance} {Principle}},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1776--1784},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a45/}
}
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A. I. Sakhanenko. On Borovkov's estimate in the Invariance Principle. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1776-1784. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a45/