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The local time of the linear self-attracting diffusion driven by weighted fractional Brownian motion

Qin Chen|Guangjun Shen|Qingbo Wang
대한수학회 (The Korean Mathematical Society)|2020.05|대한수학회보 (Bulletin of the KMS)|제57권 제3호|pp. 547-568|DOI 10.4134/BKMS.b180852

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참고문헌

키워드

Weighted fractional Brownian motionself-attracting diffusionintersection local time
주제분류수학

초록

In this paper, we introduce the linear self-attracting diffusion driven by a weighted fractional Brownian motion with weighting exponent $a>-1$ and Hurst index $|b|<a+1,0<b<1$, which is analogous to the linear fractional self-attracting diffusion. For the 1-dimensional process we study its convergence and the corresponding weighted local time. As a related problem, we also obtain the renormalized intersection local time exists in $L^2$ if $\text{max}\{a_1+b_1,a_2+b_2\}<0$.

Abstract

In this paper, we introduce the linear self-attracting diffusion driven by a weighted fractional Brownian motion with weighting exponent $a>-1$ and Hurst index $|b|<a+1,0<b<1$, which is analogous to the linear fractional self-attracting diffusion. For the 1-dimensional process we study its convergence and the corresponding weighted local time. As a related problem, we also obtain the renormalized intersection local time exists in $L^2$ if $\text{max}\{a_1+b_1,a_2+b_2\}<0$.

참고문헌 (30)

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