On uniform convergence of wavelet expansions of <I>ϕ</I>-sub-Gaussian random processes

On the uniform convergence of wavelet expansions of random processes from Orlicz spaces of random variables. I

“…Analogous results for ϕ-sub-Gaussian processes were obtained in [7]. We now briefly describe the structure of the present paper.…”

Conditions for the uniform convergence of expansions of $\varphi $-sub-Gaussian stochastic processes in function systems generated by wavelets

“…The uniform convergence of random series with probability one or in probability are considered in [2,7,9,17] and in some other papers.…”

On the distribution of storage processes from the class $V(𝜙,𝜓)$

“…Recall that V (ϕ, ψ) contains the class of ϕ-sub-Gaussian stochastic processes. More detail and results concerning the processes of V (ϕ, ψ) can be found in [3,13], and other sources are included in the list of references at the end of the paper.…”

“…Recall (see [13]) that a ϕ-sub-Gaussian process X is called stationary if 1) its norm τ ϕ (X(t)) = c ϕ = γ is constant for all t, s ∈ B, and if 2) τ ϕ (X(t) − X(s)) = σ ϕ (t − s).…”