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

  • Chen, Qin (Department of Mathematics Fuyang Normal University) ;
  • Shen, Guangjun (School of Mathematics and Finance Chuzhou University) ;
  • Wang, Qingbo (Department of Mathematics Anhui Normal University)
  • Received : 2018.09.09
  • Accepted : 2020.03.05
  • Published : 2020.05.31

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 L2 if max{a1 + b1, a2 + b2} < 0.

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