I. S. Borisov, V. A. Zhechev, “Invariance principle for canonical $U$- and $V$-statistics based on dependent observations”, Mat. Tr., 16:2 (2013), 28–44; Siberian Adv. Math., 25:1 (2015), 21

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Matematicheskie Trudy, 2013, Volume 16, Number 2, Pages 28–44 (Mi mt258)

This article is cited in 2 scientific papers (total in 2 papers)

Invariance principle for canonical

U

$U$ - and

V

$V$ -statistics based on dependent observations

I. S. Borisov^ab, V. A. Zhechev^b

^a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
^b Novosibirsk State University, Novosibirsk, Russia

Full-text PDF (238 kB) Citations (2)

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Abstract: We prove the functional limit theorem, i.e., the invariance principle, for sequences of normalized

U

$U$ - and

V

$V$ -statistics of arbitrary orders with canonical kernels, defined on samples of growing size from a stationary sequence of random variables under the

α

$\alpha$ - or

φ

$\varphi$ -mixing conditions. The corresponding limit stochastic processes are described as polynomial forms of a sequence of dependent Wiener processes with a known covariance.

Key words:

U

$U$ -statistic,

V

$V$ -statistic, invariance principle, dependent observations,

α

$\alpha$ -mixing,

φ

$\varphi$ -mixing.

Received: 27.07.2013

English version:
Siberian Advances in Mathematics, 2015, Volume 25, Issue 1, Pages 21–32
DOI: https://doi.org/10.3103/S1055134415010034

Bibliographic databases:

Document Type: Article

UDC: 519.21

Language: Russian

Citation: I. S. Borisov, V. A. Zhechev, “Invariance principle for canonical

U

$U$ - and

V

$V$ -statistics based on dependent observations”, Mat. Tr., 16:2 (2013), 28–44; Siberian Adv. Math., 25:1 (2015), 21–32

Citation in format AMSBIB

\Bibitem{BorZhe13}

\by I.~S.~Borisov, V.~A.~Zhechev

\paper Invariance principle for canonical $U$- and $V$-statistics based on dependent observations

\jour Mat. Tr.

\yr 2013

\vol 16

\issue 2

\pages 28--44

\mathnet{http://mi.mathnet.ru/mt258}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3184036}

\transl

\jour Siberian Adv. Math.

\yr 2015

\vol 25

\issue 1

\pages 21--32

\crossref{https://doi.org/10.3103/S1055134415010034}

Linking options:

https://www.mathnet.ru/eng/mt258

https://www.mathnet.ru/eng/mt/v16/i2/p28

This publication is cited in the following 2 articles:

I. S. Borisov, A. A. Bystrov, “Exponential inequalities for the distributions of canonical multiple partial sum processes”, Theory Probab. Appl., 64:2 (2019), 171–185
I. S. Borisov, V. A. Zhechev, “Exponential inequalities for the distributions of $V$ -processes based on dependent observations”, Siberian Adv. Math., 29 (2019), 263–273

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Abstract page:	485
Full-text PDF :	135
References:	104
First page:	7

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