S. M. Sadikova, “Some inequalities for characteristic functions”, Teor. Veroyatnost. i Primenen., 11:3 (1966), 500–506; Theory Probab. Appl., 11:3 (1966), 441

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Teoriya Veroyatnostei i ee Primeneniya, 1966, Volume 11, Issue 3, Pages 500–506 (Mi tvp646)

This article is cited in 11 scientific papers (total in 11 papers)

Short Communications

Some inequalities for characteristic functions

S. M. Sadikova

Moscow Engineering Physics Institute

Full-text PDF (369 kB) Citations (11)

Abstract: Let

$A$ be an oval on a plane and

$P$ the uniform distribution over

$A$ with characteristic function

$f$ . In the first part of this note an inequality for

$|f|$ is given. In the second part some inequalities for joint characteristic function of

$\xi$ and some functions of

$\xi$ are established.
The main tool used is the so-called Van der Corput lemma.

Received: 16.05.1966

English version:
Theory of Probability and its Applications, 1966, Volume 11, Issue 3, Pages 441–447
DOI: https://doi.org/10.1137/1111044

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: S. M. Sadikova, “Some inequalities for characteristic functions”, Teor. Veroyatnost. i Primenen., 11:3 (1966), 500–506; Theory Probab. Appl., 11:3 (1966), 441–447

Citation in format AMSBIB

\Bibitem{Sad66}

\by S.~M.~Sadikova

\paper Some inequalities for characteristic functions

\jour Teor. Veroyatnost. i Primenen.

\yr 1966

\vol 11

\issue 3

\pages 500--506

\mathnet{http://mi.mathnet.ru/tvp646}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=207017}

\zmath{https://zbmath.org/?q=an:0202.48803}

\transl

\jour Theory Probab. Appl.

\yr 1966

\vol 11

\issue 3

\pages 441--447

\crossref{https://doi.org/10.1137/1111044}

Linking options:

https://www.mathnet.ru/eng/tvp646

https://www.mathnet.ru/eng/tvp/v11/i3/p500

Erratum

Letter to the Editor
S. M. Sadikova
Teor. Veroyatnost. i Primenen., 1967, 12:2, 396

This publication is cited in the following 11 articles:

Avram F. Leonenko N. Sakhno L., “Limit Theorems For Additive Functionals of Stationary Fields, Under Integrability Assumptions on the Higher Order Spectral Densities”, Stoch. Process. Their Appl., 125:4 (2015), 1629–1652
F. Götze, Yu. V. Prokhorov, V. V. Ulyanov, “On smooth behavior of probability distributions under polynomial mappings”, Theory Probab. Appl., 42:1 (1998), 28–38
F. Götze, Yu. V. Prokhorov, V. V. Ulyanov, “Bounds for characteristic functions of polynomials in asymptotically normal random variables”, Russian Math. Surveys, 51:2 (1996), 181–204
Vidmantas Bentkus, Friedrich G�tze, Ri?ardas Zitikis, “Asymptotic expansions in the integral and local limit theorems in banach spaces with applications to ?-statistics”, J Theor Probab, 6:4 (1993), 727
R.J.M.M. Does, R. Helmers, C.A.J. Klaassen, “On the edgeworth expansion for the sum of a function of uniform spacings”, Journal of Statistical Planning and Inference, 17 (1987), 149
Yu. V. Borovskih, “Estimates of the characteristic functions with applications to $\omega^2$-statistics. I”, Theory Probab. Appl., 29:3 (1985), 488–503
E. M. Kudlaev, “Limiting conditional distributions for sums of random variables”, Theory Probab. Appl., 29:4 (1985), 776–786
G. I. Arkhipov, A. A. Karatsuba, V. N. Chubarikov, “Trigonometric integrals”, Math. USSR-Izv., 15:2 (1980), 211–239
V. V. Jurinskii, “Bounds for Characteristic Functions of Certain Degenerate Multidimensional Distributions”, Theory Probab. Appl., 17:1 (1972), 101–113
V. V. Yurinskiǐ, “On application of the van der Corput lemma to estimation of the characteristic functions of certain singular distributions”, Theory Probab. Appl., 16:2 (1971), 387–388
A. Bikelis, “Asymptotic expansions of the distribution functions of the sums of independent equally distributed lattice random vectors”, Theory Probab. Appl., 14:3 (1969), 481–489

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

Theory of Probability and its Applications

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