Large Time Behavior on the Linear Self-Interacting Diffusion Driven by Sub-Fractional Brownian Motion II: Self-Attracting Case
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 <...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2022-01-01
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| Series: | Frontiers in Physics |
| Subjects: | |
| Online Access: | https://www.frontiersin.org/articles/10.3389/fphy.2021.791858/full |
| Summary: | 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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| ISSN: | 2296-424X |