Large Time Behavior on the Linear Self-Interacting Diffusion Driven by Sub-Fractional Brownian Motion With Hurst Index Large Than 0.5 I: Self-Repelling Case

Gao, Han; Guo, Rui; Jin, Yang; Yan, Litan

doi:10.3389/fphy.2021.795210

Cited by 2 publications

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References 35 publications

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“…As we pointed out in the previous study (I) (see [12]), the sub-fBm S H is a rather special class of self-similar Gaussian processes such that S H 0 0 and…”

Section: Preliminariesmentioning

confidence: 68%

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Large Time Behavior on the Linear Self-Interacting Diffusion Driven by Sub-Fractional Brownian Motion II: Self-Attracting Case

et al. 2022

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In this study, as a continuation to the studies of the self-interaction diffusion driven by subfractional Brownian motion SH, we analyze the asymptotic behavior of the linear self-attracting diffusion:dXtH=dStH−θ∫0t(XtH−XsH)dsdt+νdt,X0H=0,where θ > 0 and ν∈R are two parameters. When θ < 0, the solution of this equation is called self-repelling. Our main aim is to show the solution XH converges to a normal random variable X∞H with mean zero as t tends to infinity and obtain the speed at which the process XH converges to X∞H as t tends to infinity.

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“…As we pointed out in the previous study (I) (see [12]), the sub-fBm S H is a rather special class of self-similar Gaussian processes such that S H 0 0 and…”

Section: Preliminariesmentioning

confidence: 68%

“…In a previous study (I) (see [12]), as an extension to classical result, we considered the linear selfinteracting diffusion as follows:…”

Section: Introductionmentioning

confidence: 99%

Large Time Behavior on the Linear Self-Interacting Diffusion Driven by Sub-Fractional Brownian Motion II: Self-Attracting Case

et al. 2022

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PSD and Cross-PSD of Responses of Seven Classes of Fractional Vibrations Driven by fGn, fBm, Fractional OU Process, and von Kármán Process

2024

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This paper gives its contributions in four stages. First, we propose the analytical expressions of power spectrum density (PSD) responses and cross-PSD responses to seven classes of fractional vibrators driven by fractional Gaussian noise (fGn). Second, we put forward the analytical expressions of PSD and cross-PSD responses to seven classes of fractional vibrators excited by fractional Brownian motion (fBm). Third, we present the analytical expressions of PSD and cross-PSD responses to seven classes of fractional vibrators driven by the fractional Ornstein–Uhlenbeck (OU) process. Fourth, we bring forward the analytical expressions of PSD and cross-PSD responses to seven classes of fractional vibrators excited by the von Kármán process. We show that the statistical dependences of the responses to seven classes of fractional vibrators follow those of the excitation of fGn, fBm, the OU process, or the von Kármán process. We also demonstrate the obvious effects of fractional orders on the responses to seven classes of fractional vibrations. In addition, we newly introduce class VII fractional vibrators, their frequency transfer function, and their impulse response in this research.

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Large Time Behavior on the Linear Self-Interacting Diffusion Driven by Sub-Fractional Brownian Motion With Hurst Index Large Than 0.5 I: Self-Repelling Case

Cited by 2 publications

References 35 publications

Large Time Behavior on the Linear Self-Interacting Diffusion Driven by Sub-Fractional Brownian Motion II: Self-Attracting Case

Large Time Behavior on the Linear Self-Interacting Diffusion Driven by Sub-Fractional Brownian Motion II: Self-Attracting Case

PSD and Cross-PSD of Responses of Seven Classes of Fractional Vibrations Driven by fGn, fBm, Fractional OU Process, and von Kármán Process

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