Supremum Distribution of Weighted Sum of Random Processes from Orlicz Spaces of Exponential Type with Continuous Deviation

The paper studies distribution of sum random processes from Orlicz spaces exponential type weighted by continuous functions, in particular, Subϕ (Ω), SSubϕ (Ω) and class V (ϕ, ψ) are considered. Such classes variables corresponding stochastic provide generalizations Gaussian sub-Gaussian important for various applications, example, queuing theory financial mathematics. We derive the estimates supremum such deviated a monotone function using entropy method. As examples, Wiener fractional Brownian motion with different Hurst indices Corresponding probability exceeding trajectories sums positive level determined linear obtained. In insurance risk theory, aproblem arises during estimating ruin process constant premium income, communications it appears buffer overflow single server service rate.