Abstract
Let \(B^{H_i ,K_i } = \{ B_t^{H_i ,K_i } ,t \geqslant 0\} \), i = 1, 2 be two independent bifractional Brownian motions with respective indices H i ∈ (0, 1) and K i ∈ (0, 1]. One of the main motivations of this paper is to investigate the smoothness of the collision local time, introduced by Jiang and Wang in 2009, \(\ell _T = \int_0^T {\delta (B_s^{H_1 ,K_1 } - B_s^{H_2 ,K_2 } )ds} \) T > 0, where δ denotes the Dirac delta function. By an elementary method, we show that ℓ T is smooth in the sense of the Meyer-Watanabe if and only if min{H 1 K 1, H 2 K 2} < 1/3.
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Shen, G., Yan, L. Smoothness for the collision local times of bifractional Brownian motions. Sci. China Math. 54, 1859–1873 (2011). https://doi.org/10.1007/s11425-011-4228-3
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DOI: https://doi.org/10.1007/s11425-011-4228-3