The paper studies distribution of sum of random processes from Orlicz spaces of exponential
type weighted by continuous functions, in particular, processes from spaces Subϕ (Ω), …

In this paper we consider random process from the space Subϕ (Ω)(space of ϕ-sub-Gaussian
random variables) defined on compact set and the probability that this process exceeds …

It is well known that often the one-dimensional distribution of a queue content is not Gaussian
but its tails behave like a Gaussian. We propose to consider a general class of processes, …

The paper is devoted to the study of sub-Gaussian random variables and stochastic processes.
Recall that along with centered Gaussian random variables the space Sub(Ω) of sub-…

In this paper we investigate the ruin problem for the generalized φ-sub-Gaussian fractional
Brownian motion (FBM). Such random process has the same covariation function as FBM but …

This paper is devoted to investigation of supremum of averaged deviations $| X (t)-f (t)-\int _ {\mathbb
{T}}(X (u)-f (u))\hspace {0.1667 em}\mathrm {d}\mu (u)/\mu (\mathbb {T})| $ of a …

The chapter is devoted to investigation of the class $$V (\varphi,\psi )$$ of $$\varphi$$ -sub-Gaussian
random processes with application to queueing theory. This class of stochastic …

In this paper we consider random process from the space Subϕ (Ω), which is defined on
compact set, and the probability that supremum of this process exceeds some function. The …

Random processes from the class V (φ, ψ) which is more general than the class of ψ-sub-Gaussian
random process. The upper estimate of the probability that a random process from …

We consider the process\[A (t)= mt+\sigma\int _0^ t X (u) du,\qquad t\geq 0,\] describing the
queue length, where $ m $ and $\sigma $ are positive constants, $ X (u) $ is a $\varphi $-sub-…