The distribution of the supremum of preGaussian shot noise processes
Authors:
Yu. V. Kozachenko and I. V. Dariĭchuk
Translated by:
Oleg Klesov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom 80 (2009).
Journal:
Theor. Probability and Math. Statist. 80 (2010), 85100
MSC (2000):
Primary 60G20; Secondary 60G60
Published electronically:
August 19, 2010
MathSciNet review:
2541954
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Abstract: Estimates for the distribution of the supremum of preGaussian shot noise stochastic processes are obtained in the paper for both cases of finite and infinite intervals.
 1.
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
(2001g:60089)
 2.
Illya
Dariychuk and Yurij
Kozachenko, Estimates for the distribution of the supremum of
ΘpreGaussian random processes, Random Oper. Stoch. Equ.
16 (2008), no. 1, 39–78. MR 2404275
(2009m:60123), 10.1515/ROSE.2008.004
 3.
I.
V. Dariychuk, Uniformly convergence of wavelet expansions of
ΘpreGaussian random processes, Nauk. Vīsn. Uzhgorod.
Univ. Ser. Mat. Īnform. 16 (2008), 62–72
(English, with English and Ukrainian summaries). MR 2581408
(2010m:60111)
 4.
Yu.
V. Kozachenko and O.
I. Livins′ka, Analytic properties of certain classes of
stochastic processes from the space
𝑃𝑟𝑒𝑑ᵩ(Ω), Teor.
Ĭmovīr. Mat. Stat. 51 (1994), 90–97
(Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math.
Statist. 51 (1995), 93–101 (1996). MR 1445056
(98a:60044)
 5.
V. V. Buldygin, On some properties of the generalized Schottky effect processes, Proceedings of the Second UkrainianHungarian Conference ``New Trends in Probability and Statistics'', TViMS, Kiev, 1992, pp. 1333.
 6.
V.
V. Buldygin and V.
G. Shportyuk, On the normalization of random fields represented by
stochastic integrals over fields with independent increments, Teor.
Ĭmovīr. Mat. Stat. 49 (1993), 65–81
(Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math.
Statist. 49 (1994), 47–58 (1995). MR 1445247
(97m:60071)
 7.
V.
V. Buldygin and N.
V. Yarovaya, A functional limit theorem for shot noise fields,
Problems of the theory of probability distributions, Akad. Nauk Ukrain.
SSR, Inst. Mat., Kiev, 1983, pp. 25–41 (Russian). MR 745465
(86a:60045)
 8.
V.
V. Buldygin and N.
V. Yarovaya, Cumulant conditions for the continuity of random
processes, Dokl. Akad. Nauk Ukrain. SSR Ser. A 2
(1990), 3–6, 83 (Russian, with English summary). MR 1054037
(91e:60127)
 9.
A.
V. Skorokhod, Sluchainye protsessy s nezavisimymi
prirashcheniyami, 2nd ed., \cyr Teoriya Veroyatnosteĭ\ i
Matematicheskaya Statistika. [Probability Theory and Mathematical
Statistics], “Nauka”, Moscow, 1986 (Russian). MR 860563
(88b:60171)
 1.
 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)
 2.
 I. V. Dariychuk and Yu. V. Kozachenko Estimates for the distribution of the supremum of preGaussian random processes, Random Oper. Stoch. Equ. 16 (2008), no. 2, 3978. MR 2404275 (2009m:60123)
 3.
 I. V. Dariychuk Uniform convergence of wavelet expansions of preGaussian random processes, Naukovyi Visnyk, Uzhgorod University 16 (2008), 6272. (Ukrainian) MR 2581408
 4.
 Yu. V. Kozachenko and O. I. Livins'ka Analytic properties of certain classes of stochastic processes from the space , Teor. Imovirnost. Mat. Stat. 51 (1994), 9097; English transl. in Theor. Probability and Math. Statist. 51 (1995), 93101. MR 1445056 (98a:60044)
 5.
 V. V. Buldygin, On some properties of the generalized Schottky effect processes, Proceedings of the Second UkrainianHungarian Conference ``New Trends in Probability and Statistics'', TViMS, Kiev, 1992, pp. 1333.
 6.
 V. V. Buldygin and V. G. Shportyuk, On a normalization of random fields represented by stochastic integrals over fields with independent increments, Teor. Imovirnost. Mat. Stat. 49 (1993), 6582; English transl. in Theor. Probability and Math. Statist. 49 (1994), 4758. MR 1445247 (97m:60071)
 7.
 V. V. Buldygin and N. V. Yarovaya, A functional limit theorem for fields, Problems of the Theory of Probability Distributions, Institute of Mathematics, Academy of Science of Ukrainian SSR, Kiev, 1983, pp. 2541. (Russian) MR 745465 (86a:60045)
 8.
 V. V. Buldygin and N. V. Yarovaya Semiinvariant conditions for the continuity of stochastic processes, Dokl. Akad. Nauk Ukr. SSR, Ser. A 2 (1990), 36. (Russian) MR 1054037 (91e:60127)
 9.
 A. V. Skorokhod, Random Processes with Independent Increments, Nauka, Moscow, 1986; English transl., Kluwer Academic Publishers, Dordrecht, 1991. MR 860563 (88b:60171)
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Additional Information
Yu. V. Kozachenko
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 2, Kiev 03127, Ukraine
Email:
yvk@univ.kiev.ua
I. V. Dariĭchuk
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 2, Kiev 03127, Ukraine
Email:
elijadar@rambler.ru
DOI:
http://dx.doi.org/10.1090/S009490002010007964
Keywords:
$\Theta$preGaussian stochastic processes,
shot noise processes
Received by editor(s):
November 7, 2008
Published electronically:
August 19, 2010
Article copyright:
© Copyright 2010
American Mathematical Society
