Properties of Some Random Series

This paper is devoted to the investigation of conditions for the weak convergence in the space C(T) of the stochastic processes from the space F ψ (Ω). Using these conditions the limit theorem for stochastic processes from the space F ψ (Ω) is obtained. This theorem can be utilized for achieving the given approximation accuracy and reliability of integrals depending on parameter by Monte Carlo method.

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“…Let us check the condition (7). For the space F ψ (Ω), where ψ(u) = u 1 2 the majorant characteristic has the form (see [8,9,10])…”

Section: Weak Convergence Of Stochastic Processes From Spaces F ψ (ω)mentioning

confidence: 99%

“…Estimates for the distribution of suprema for the Gaussian stochastic processes can be found in books [3,16] and papers [2,6]. Some applications of these results are presented in [7,13]. The probabilities of large deviations for the sums of independent stochastic processes from the space F ψ (Ω) are considered in the paper [9].…”

Section: Introductionmentioning

confidence: 99%

Weak convergence of stochastic processes from spaces $F_\psi(\Omega)$

Млавець

Kozachenko

Yurchenko

2018

Stat., optim. inf. comput.

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“…Theorem 3.1. (Kozachenko et al (2011)) Suppose that { ( ), ∈ } is a centered second-order random process with the correlation function ( , ) = E ( ) ( ), ( , ℬ , ) is a measure space, { ( ), ∈ ℤ} is an orthonormal basis in 2 ( , ) and ( ,⋅) ∈ 2 ( , ), ∈ .…”

Section: A Wavelet-based Expansionmentioning

confidence: 99%

A New Wavelet-based Expansion of a Random Process

Turchyn¹

2016

JAMS

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“…In particular, wavelet-based simulation and series expansions of stochastic processes have been studied by Wornell (1993), Meyer et al (1999), Whitcher (2001), Seleznjev and Staroverov (2002), Ayache and Taqqu (2003), Pipiras (2004Pipiras ( , 2005. Wavelet-based expansions of stochastic processes in series with uncorrelated terms have been researched by Walter and Zhang (1994), Didier and Pipiras (2008), Kozachenko et al (2011).…”

Section: Introductionmentioning

confidence: 99%