Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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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
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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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Acknowledgement

This research is supported by the Distinguished Young Scholars Foundation of Anhui Province (1608085J06), the National Natural Science Foundation of China (11271020). The authors are very grateful to the anonymous referee and the editor for their insightful and valuable comments, which have improved the presentation of the paper.

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