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*, 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 -pre-Gaussian random processes*, Random Oper. Stoch. Equ.**16**(2008), no. 2, 39-78. MR**2404275 (2009m:60123)****3.**I. V. Dariychuk*Uniform convergence of wavelet expansions of -pre-Gaussian random processes*, Naukovyi Visnyk, Uzhgorod University**16**(2008), 62-72. (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), 90-97; English transl. in Theor. Probability and Math. Statist.**51**(1995), 93-101. MR**1445056 (98a:60044)****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 a normalization of random fields represented by stochastic integrals over fields with independent increments*, Teor. Imovirnost. Mat. Stat.**49**(1993), 65-82; English transl. in Theor. Probability and Math. Statist.**49**(1994), 47-58. 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. 25-41. (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), 3-6. (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:
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