2009
DOI: 10.1090/s0094-9000-09-00764-9
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Conditions for the uniform convergence of expansions of $\varphi $-sub-Gaussian stochastic processes in function systems generated by wavelets

Abstract: Abstract. The expansions with uncorrelated coefficients in function systems generated by wavelets are constructed in the paper for second order stochastic processes. Conditions for the uniform convergence with probability one on a finite interval are found for expansions whose coefficients are independent. Conditions for the uniform convergence in probability on a finite interval are found for expansions of strictly ϕ-sub-Gaussian stochastic processes.

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Cited by 3 publications
(5 citation statements)
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References 12 publications
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“…This result is a counterpart of a theorem proved in Kozachenko and Turchin (2009) for stationary processes.…”
Section: Discussionsupporting
confidence: 58%
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“…This result is a counterpart of a theorem proved in Kozachenko and Turchin (2009) for stationary processes.…”
Section: Discussionsupporting
confidence: 58%
“…Conditions for uniform convergence with probability 1 of such expansion for stochastic processes from a wide class which includes stationary and non-stationary processes are obtained. This result is a counterpart of a theorem from Kozachenko and Turchin (2009), where only stationary processes were considered. …”
mentioning
confidence: 63%
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