The distribution of the supremum of -pre-Gaussian 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), 85-100

MSC (2000):
Primary 60G20; Secondary 60G60

DOI:
https://doi.org/10.1090/S0094-9000-2010-00796-4

Published electronically:
August 19, 2010

MathSciNet review:
2541954

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Estimates for the distribution of the supremum of -pre-Gaussian 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****2.**Illya Dariychuk and Yurij Kozachenko,*Estimates for the distribution of the supremum of Θ-pre-Gaussian random processes*, Random Oper. Stoch. Equ.**16**(2008), no. 1, 39–78. MR**2404275**, https://doi.org/10.1515/ROSE.2008.004**3.**I. V. Dariychuk,*Uniformly convergence of wavelet expansions of Θ-pre-Gaussian random processes*, Nauk. Vīsn. Uzhgorod. Univ. Ser. Mat. Īnform.**16**(2008), 62–72 (English, with English and Ukrainian summaries). MR**2581408****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****5.**V. V. Buldygin,*On some properties of the generalized Schottky effect processes*, Proceedings of the Second Ukrainian-Hungarian Conference ``New Trends in Probability and Statistics'', TViMS, Kiev, 1992, pp. 13-33.**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****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****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****9.**A. V. Skorokhod,*Sluchaĭ nye protsessy s nezavisimymi prirashcheniyami*, 2nd ed., Teoriya Veroyatnosteĭ i Matematicheskaya Statistika. [Probability Theory and Mathematical Statistics], “Nauka”, Moscow, 1986 (Russian). MR**860563**

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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:
https://doi.org/10.1090/S0094-9000-2010-00796-4

Keywords:
$\Theta$-pre-Gaussian stochastic processes,
shot noise processes

Received by editor(s):
November 7, 2008

Published electronically:
August 19, 2010

Article copyright:
© Copyright 2010
American Mathematical Society