Convergence in $L_p([0,T])$ of wavelet expansions of $\varphi$-sub-Gaussian random processes
Yuriy Kozachenko (1), Andriy Olenko (2), Olga Polosmak (3) ((1), Department of Probability Theory, Statistics, Actuarial Mathematics, Kyiv, University, Kyiv, Ukraine (2) Department of Mathematics, Statistics, La, Trobe University, Victoria
TL;DR
This paper investigates the convergence properties of wavelet expansions for $\
Contribution
It provides new results on convergence in $L_p([0,T])$ for wavelet expansions of $\\varphi$-sub-Gaussian processes, including convergence rates.
Findings
Convergence in $L_p([0,T])$ is established for wavelet expansions.
Explicit convergence rates are derived.
Results are applicable to a broad class of $\\varphi$-sub-Gaussian processes.
Abstract
The article presents new results on convergence in of wavelet expansions of -sub-Gaussian random processes. The convergence rate of the expansions is obtained. Specifications of the obtained results are discussed.
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Taxonomy
TopicsAnalysis of environmental and stochastic processes