The distribution of the supremum of $\Theta$-pre-Gaussian shot noise processes
Authors:
Yu. V. Kozachenko and I. V. Dariĭchuk
Translated by:
Oleg Klesov
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 $\Theta$-pre-Gaussian shot noise stochastic processes are obtained in the paper for both cases of finite and infinite intervals.
References
- 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
- Illya Dariychuk and Yurij Kozachenko, Estimates for the distribution of the supremum of $\Theta $-pre-Gaussian random processes, Random Oper. Stoch. Equ. 16 (2008), no. 1, 39–78. MR 2404275, DOI https://doi.org/10.1515/ROSE.2008.004
- I. V. Dariychuk, Uniformly convergence of wavelet expansions of $\Theta $-pre-Gaussian random processes, Nauk. Vīsn. Uzhgorod. Univ. Ser. Mat. Īnform. 16 (2008), 62–72 (English, with English and Ukrainian summaries). MR 2581408
- Yu. V. Kozachenko and O. I. Livins′ka, Analytic properties of certain classes of stochastic processes from the space ${\rm Pred}_\phi (\Omega )$, 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
- 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.
- 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
- 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
- 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
- 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
References
- 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)
- I. V. Dariychuk and Yu. V. Kozachenko Estimates for the distribution of the supremum of $\Theta$-pre-Gaussian random processes, Random Oper. Stoch. Equ. 16 (2008), no. 2, 39–78. MR 2404275 (2009m:60123)
- I. V. Dariychuk Uniform convergence of wavelet expansions of $\Theta$-pre-Gaussian random processes, Naukovyi Visnyk, Uzhgorod University 16 (2008), 62–72. (Ukrainian) MR 2581408
- Yu. V. Kozachenko and O. I. Livins’ka Analytic properties of certain classes of stochastic processes from the space $\operatorname {Pred}_{\varphi }(\Omega )$, Teor. Imovirnost. Mat. Stat. 51 (1994), 90–97; English transl. in Theor. Probability and Math. Statist. 51 (1995), 93–101. MR 1445056 (98a:60044)
- 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.
- 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)
- V. V. Buldygin and N. V. Yarovaya, A functional limit theorem for \shotnoise 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)
- 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)
- A. V. Skorokhod, Random Processes with Independent Increments, Nauka, Moscow, 1986; English transl., Kluwer Academic Publishers, Dordrecht, 1991. MR 860563 (88b:60171)
Similar Articles
Retrieve articles in Theory of Probability and Mathematical Statistics
with MSC (2000):
60G20,
60G60
Retrieve articles in all journals
with MSC (2000):
60G20,
60G60
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
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
