Self-intersection local times and collision local times of bifractional Brownian motions
Local times on fractional Brownian motions have been studied by many researchers [see e.g. \textit{A. Ayache, D. Wu} and \textit{Y. Xiao}, Ann. Inst. Henri Poincaré, Probab. Stat. 44, No. 4, 727--748 (2008; Zbl 1180.60032), \textit{Y. Jiang} and \textit{Y. Wang}, Chin. Ann. Math., Ser. B 28, No. 3, 311--320 (2007; Zbl 1124.60036)]. In this paper, the authors consider the local time and the self-intersection local time for a bifractional Brownian motion, and the collision local time for two independent bifractional Brownian motions. They mainly prove the existence and smoothness of the self-intersection local time and the collision local time, through the strong local nondeterminism of bifractional Brownian motion, \(L^{2}\) convergence and Chaos expansion.
scientific article; zbMATH DE number 5645744
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