Bounds for the distribution of some functionals of processes with -sub-Gaussian increments

Author:
R. E. Yamnenko

Translated by:
S. Kvasko

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **85** (2011).

Journal:
Theor. Probability and Math. Statist. **85** (2012), 181-197

MSC (2000):
Primary 60G07; Secondary 60K25

DOI:
https://doi.org/10.1090/S0094-9000-2013-00884-9

Published electronically:
January 14, 2013

MathSciNet review:
2933713

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Bounds for the distribution of some functionals of a stochastic process belonging to the class are obtained. An example of the functionals studied in the paper is given by

**1.**R. Addie, P. Mannersalo, and I. Norros,*Most probable paths and performance formulae for buffers with Gaussian input traffic*, Eur. Trans. Telecommun.**13(3)**(2002), 183-196.**2.**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****3.**Yu. Kozachenko, T. Sottīnen, and O. Vasilik,*Self-similar processes with stationary increments in the spaces 𝑆𝑆𝑢𝑏ᵩ(Ω)*, Teor. Ĭmovīr. Mat. Stat.**65**(2001), 67–78 (Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math. Statist.**65**(2002), 77–88. MR**1936131****4.**Olga Vasylyk, Yuriy Kozachenko, and Rostyslav Yamnenko,*Upper estimate of overrunning by 𝑆𝑢𝑏ᵩ(Ω) random process the level specified by continuous function*, Random Oper. Stochastic Equations**13**(2005), no. 2, 111–128. MR**2152102**, https://doi.org/10.1163/156939705323383832**5.**I. Norros,*On the use of fractional Brownian motions in the theory of connectionless networks*, IEEE Journal on Selected Areas in Communications**13**(1995), no. 6, 953-962.**6.**Rostyslav Yamnenko,*Ruin probability for generalized 𝜙-sub-Gaussian fractional Brownian motion*, Theory Stoch. Process.**12**(2006), no. 3-4, 261–275. MR**2316577****7.**Rostyslav Yamnenko and Olga Vasylyk,*Random process from the class 𝑉(𝜙,𝜓): exceeding a curve*, Theory Stoch. Process.**13**(2007), no. 4, 219–232. MR**2482262****8.**Yu. Kozachenko, O. I. Vasylyk, and R. E. Yamnenko,*-sub-Gaussian Random Processes*, ``Kyiv University'', Kyiv, 2008. (Ukrainian)**9.**R. Ē. Yamnenko and O. S. Shramko,*On the distribution of storage processes from the class 𝑉(𝜙,𝜓)*, Teor. Ĭmovīr. Mat. Stat.**83**(2010), 163–176 (Ukrainian, with English, Russian and Ukrainian summaries); English transl., Theory Probab. Math. Statist.**83**(2011), 191–206. MR**2768858**, https://doi.org/10.1090/S0094-9000-2012-00851-X

Retrieve articles in *Theory of Probability and Mathematical Statistics*
with MSC (2000):
60G07,
60K25

Retrieve articles in all journals with MSC (2000): 60G07, 60K25

Additional Information

**R. E. Yamnenko**

Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 2, Kiev 03127, Ukraine

Email:
yamnenko@univ.kiev.ua

DOI:
https://doi.org/10.1090/S0094-9000-2013-00884-9

Keywords:
Generalized fractional Brownian motion,
metric entropy,
queue,
bounds for the distribution,
sub-Gaussian process

Received by editor(s):
June 11, 2011

Published electronically:
January 14, 2013

Article copyright:
© Copyright 2013
American Mathematical Society