2011
DOI: 10.1515/mcma.2011.010
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Simulation of sub-Gaussian processes using wavelets

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Cited by 7 publications
(5 citation statements)
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“…We prove a theorem about simulation of a Gaussian process with given accuracy and reliability in ([0, ]) using this wavelet-based model and the Haar wavelet. Analogous results about simulation of Gaussian and sub-Gaussian processes with given accuracy and reliability by means of a similar model have been obtained before in Kozachenko and Turchyn (2008) and Turchyn (2011). Our result is valid for a wide class of Gaussian processes, this class includes certain processes to which earlier theorems about simulation with given accuracy and reliability using similar wavelet-based models are not applicable.…”
Section: Introductionsupporting
confidence: 83%
“…We prove a theorem about simulation of a Gaussian process with given accuracy and reliability in ([0, ]) using this wavelet-based model and the Haar wavelet. Analogous results about simulation of Gaussian and sub-Gaussian processes with given accuracy and reliability by means of a similar model have been obtained before in Kozachenko and Turchyn (2008) and Turchyn (2011). Our result is valid for a wide class of Gaussian processes, this class includes certain processes to which earlier theorems about simulation with given accuracy and reliability using similar wavelet-based models are not applicable.…”
Section: Introductionsupporting
confidence: 83%
“…The upper estimate of overrunning the level specified by the continuous function by Sub φ (Ω) stochastic process was obtained in [16]. The theory of φ-sub-Gaussian processes was successfully applied in the wavelets theory [27], the signal theory [10,21,22] and other areas of research [1,2,7,13,14,19,20,26,28].…”
Section: Introductionmentioning
confidence: 99%
“…Lemma 4.1. ( [8]) Let X = {X(t), t ∈ R} be a centered stochastic process which satisfies the requirements of Theorem 2.1, T > 0, φ be a scaling function, ψ be the corresponding wavelet, the function φ(y) be absolutely continuous on any interval, the function u(t, y) be absolutely continuous with respect to y for any fixed t, there exist the derivatives u ′ λ (t, λ), φ′ (y), ψ′ (y)…”
Section: Simulation With Given Relative Accuracy and Reliability In C...mentioning
confidence: 99%
“…Lemma 4.2. ( [8]) Let X = {X(t), t ∈ R} be a centered stochastic process which satisfies the requirements of Theorem 2.1, T > 0, φ be a scaling function, ψ be the corresponding wavelet, S(y) = ψ(y), S φ (y) = φ(y); φ(y), u(t, λ), S(y), S φ (y) satisfy such conditions: the function u(t, y) is absolutely continuous with respect to y, the function φ(y) is absolutely continuous,…”
Section: Simulation With Given Relative Accuracy and Reliability In C...mentioning
confidence: 99%