• Title/Summary/Keyword: Weighted fractional Brownian motion

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THE LOCAL TIME OF THE LINEAR SELF-ATTRACTING DIFFUSION DRIVEN BY WEIGHTED FRACTIONAL BROWNIAN MOTION

  • Chen, Qin;Shen, Guangjun;Wang, Qingbo
    • Bulletin of the Korean Mathematical Society
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    • v.57 no.3
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    • pp.547-568
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    • 2020
  • 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 L2 if max{a1 + b1, a2 + b2} < 0.