The distribution of the supremum of a -reflected stochastic process with an input process belonging to some exponential type Orlicz space

Author:
R. E. Yamnenko

Translated by:
S. Kvasko

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **94** (2016).

Journal:
Theor. Probability and Math. Statist. **94** (2017), 185-201

MSC (2010):
Primary 60G07; Secondary 60K25

DOI:
https://doi.org/10.1090/tpms/1017

Published electronically:
August 25, 2017

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Abstract | References | Similar Articles | Additional Information

Abstract: The paper is devoted to the study of properties of a -reflected process with an input belonging to some exponential type Orlicz space. In particular, sub-Gaussian and -sub-Gaussian whose input processes belong to some of the general classes are studied. The -reflected process is a stochastic process of the form

Some upper bounds for the ruin probability are considered in the corresponding risk model for all . The results obtained in the paper are applied for the case of the sub-Gaussian generalized fractional Brownian motion.

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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, 6, Kyiv 03127, Ukraine

Email:
yamnenko@univ.kiev.ua

DOI:
https://doi.org/10.1090/tpms/1017

Keywords:
Generalized fractional Brownian motion,
metric entropy,
an estimate of the distribution,
sub-Gaussian process,
Orlicz space

Received by editor(s):
March 21, 2016

Published electronically:
August 25, 2017

Article copyright:
© Copyright 2017
American Mathematical Society