Abstract:
Probability distribution concentrated on k-dimensional smooth surfaces in Rm are shown to possess characteristic functions which decrease like negative powers of the norm of their argument (the latter tending to infinity) if they are generated by bounded surface densities satisfying a Lipschitz condition and the surface (support of the distribution) has no contacts of arbitrarily high order with (m−1)-dimensional hyperplanes in Rm.
Citation:
V. V. Jurinskii, “Bounds for Characteristic Functions of Certain Degenerate Multidimensional Distributions”, Teor. Veroyatnost. i Primenen., 17:1 (1972), 99–110; Theory Probab. Appl., 17:1 (1972), 101–113
\Bibitem{Yur72}
\by V.~V.~Jurinskii
\paper Bounds for Characteristic Functions of Certain Degenerate Multidimensional Distributions
\jour Teor. Veroyatnost. i Primenen.
\yr 1972
\vol 17
\issue 1
\pages 99--110
\mathnet{http://mi.mathnet.ru/tvp4192}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1109018}
\zmath{https://zbmath.org/?q=an:0273.60007}
\transl
\jour Theory Probab. Appl.
\yr 1972
\vol 17
\issue 1
\pages 101--113
\crossref{https://doi.org/10.1137/1117008}
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https://www.mathnet.ru/eng/tvp4192
https://www.mathnet.ru/eng/tvp/v17/i1/p99
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Yu. V. Borovskih, “Estimates of the characteristic functions with applications to ω2-statistics. I”, Theory Probab. Appl., 29:3 (1985), 488–503
J. PFANZAGL, Developments in Statistics, 3, 1980, 1
G. I. Arkhipov, A. A. Karatsuba, V. N. Chubarikov, “Trigonometric integrals”, Math. USSR-Izv., 15:2 (1980), 211–239
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D. M. Chibisov, “An asymptotic expansion for the distribution of a statistic admitting an asymptotic expansion”, Theory Probab. Appl., 17:4 (1973), 620–630
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