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Self-intersection local times and collision local times of bifractional Brownian motions. (English) Zbl 1181.60059

Local times on fractional Brownian motions have been studied by many researchers [see e.g. A. Ayache, D. Wu and Y. Xiao, Ann. Inst. Henri Poincaré, Probab. Stat. 44, No. 4, 727–748 (2008; Zbl 1180.60032), Y. Jiang and 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.

MSC:

60G15 Gaussian processes
60G18 Self-similar stochastic processes
60J55 Local time and additive functionals
60G22 Fractional processes, including fractional Brownian motion
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