Bounds for the distribution of some functionals of processes with subGaussian 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), 181197
MSC (2000):
Primary 60G07; Secondary 60K25
Published electronically:
January 14, 2013
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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 where is a continuous function that can be viewed as a service output rate of a queue formed by the process . For the latter interpretation, the bounds can be viewed as upper estimates for the buffer overflow probabilities with buffer size . The results obtained in the paper apply to Gaussian stochastic processes. As an example, we show an application for the generalized fractional Brownian motion defined on a finite interval.
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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:
http://dx.doi.org/10.1090/S009490002013008849
PII:
S 00949000(2013)008849
Keywords:
Generalized fractional Brownian motion,
metric entropy,
queue,
bounds for the distribution,
subGaussian process
Received by editor(s):
June 11, 2011
Published electronically:
January 14, 2013
Article copyright:
© Copyright 2013 American Mathematical Society
