Inequalities for the distributions of functionals of sub-Gaussian vectors
Authors:
V. V. Buldygin and E. D. Pechuk
Translated by:
Oleg Klesov
Journal:
Theor. Probability and Math. Statist. 80 (2010), 25-36
MSC (2000):
Primary 60G60, 60G17
DOI:
https://doi.org/10.1090/S0094-9000-2010-00792-7
Published electronically:
August 18, 2010
MathSciNet review:
2541949
Full-text PDF Free Access
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Additional Information
Abstract: Exponential inequalities for moment generating functions and for distributions of sub-Gaussian random vectors are studied in the paper.
References
- Ryoji Fukuda, Exponential integrability of sub-Gaussian vectors, Probab. Theory Related Fields 85 (1990), no. 4, 505–521. MR 1061942, DOI https://doi.org/10.1007/BF01203168
- V. V. Buldygin and Yu. V. Kozachenko, Metric characterization of random variables and random processes, Translations of Mathematical Monographs, vol. 188, American Mathematical Society, Providence, RI, 2000. Translated from the 1998 Russian original by V. Zaiats. MR 1743716
- R. Giuliano Antonini, Exponential bounds for the distribution for the norm of scalarly subgaussian random vectors, Sezione di analisi matematica e probabilita, vol. 2.240.957, Universita di Pisa, Maggio, 1996.
- R. Dzhīulīano, Yu. V. Kozachenko, and A. M. Tegza, Inequalities for the norms of sub-Gaussian vectors and the accuracy of the modeling of random processes, Teor. Ĭmovīr. Mat. Stat. 66 (2002), 58–66 (Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math. Statist. 66 (2003), 63–72. MR 1931677
- R. Giuliano Antonini and Yu. V. Kozachenko, A note on the asymptotic behavior of sequences of generalized subGaussian random vectors, Random Oper. Stochastic Equations 13 (2005), no. 1, 39–52. MR 2130246, DOI https://doi.org/10.1163/1569397053300900
- N. N. Vakhaniya, V. V. Kvaratskheliya, and V. I. Tarieladze, Weakly sub-Gaussian random elements in Banach spaces, Ukraïn. Mat. Zh. 57 (2005), no. 9, 1187–1208 (Russian, with English and Ukrainian summaries); English transl., Ukrainian Math. J. 57 (2005), no. 9, 1387–1412. MR 2216040, DOI https://doi.org/10.1007/s11253-006-0003-y
- V. I. Bogachev, Gaussovskie mery, Fizmatlit “Nauka”, Moscow, 1997 (Russian, with Russian summary). MR 1663929
References
- R. Fukuda, Exponential integrability of sub-Gaussian vectors, Probab. Theory Relat. Fields 85 (1990), no. 4, 505–521. MR 1061942 (92e:60005)
- V. V. Buldygin and Yu. V. Kozachenko, Metric Characterization of Random Variables and Random Processes, TViMS, Kiev, 1998; English transl., American Mathematical Society, Providence, RI, 2000. MR 1743716 (2001g:60089)
- R. Giuliano Antonini, Exponential bounds for the distribution for the norm of scalarly subgaussian random vectors, Sezione di analisi matematica e probabilita, vol. 2.240.957, Universita di Pisa, Maggio, 1996.
- R. Giuliano Antonini, Yu. V. Kozachenko, and A. M. Tegza, Inequalities for the norms of sub-Gaussian vectors and the accuracy of the modeling of random processes, Teor. Imovirnost. Matem. Statist. 66 (2002), 58–66; English transl in. Theory Probab. Math. Stat. 66 (2003), 63–72. MR 1931677 (2003h:60053)
- R. Giuliano Antonini and Yu. V. Kozachenko, A note on the asymptotic behavior of sequences of generalized sub-Gaussian random vectors, Rand. Oper. Stoch. Equ. 13 (2005), no. 1, 39–52. MR 2130246 (2006b:60020)
- N. N. Vakhaniya, V. V. Kvaratskheliya, and V. I. Tarieladze, Weakly sub-Gaussian random elements in Banach spaces, Ukr. Mat. Zh. 57 (2005), no. 9, 1187–1208; English transl. in Ukr. Math. J. 57 (2005), no. 9, 1387–1412. MR 2216040 (2007c:60006)
- V. I. Bogachev, Gaussian Measures, Nauka, Moscow, 1997; English transl. in American Mathematical Society, Providence, RI, 1998. MR 1663929 (2000b:60097); MR1642391 (2000a:60004)
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Additional Information
V. V. Buldygin
Affiliation:
Department of Mathematical Analysis and Probability Theory, Faculty for Physics and Mathematics, National Technical University of Ukraine “KPI”, Peremogy Avenue, 37, Kiev 03056, Ukraine
Email:
matan@ntu-kpi.kiev.ua
E. D. Pechuk
Affiliation:
Department of Mathematical Analysis and Probability Theory, Faculty for Physics and Mathematics, National Technical University of Ukraine “KPI”, Peremogy Avenue, 37, Kiev 03056, Ukraine
Email:
matan@ntu-kpi.kiev.ua
Keywords:
Sub-Gaussian random vectors,
distributions of functionals,
exponential inequalities
Received by editor(s):
November 17, 2008
Published electronically:
August 18, 2010
Article copyright:
© Copyright 2010
American Mathematical Society
