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Keywords:
bifractional Brownian motion; collision local time; intersection local time; chaos expansion
Summary:
Let $B^{H_{i},K_i}=\{B^{H_{i},K_i}_t, t\geq 0 \}$, $i=1,2$ be two independent, $d$-dimensional bifractional Brownian motions with respective indices $H_i\in (0,1)$ and $K_i\in (0,1]$. Assume $d\geq 2$. One of the main motivations of this paper is to investigate smoothness of the collision local time $$ \ell _T=\int _{0}^{T}\delta (B_{s}^{H_{1},K_1}-B_{s}^{H_{2},K_2}) {\rm d} s, \qquad T>0, $$ where $\delta $ denotes the Dirac delta function. By an elementary method we show that $\ell _T$ is smooth in the sense of Meyer-Watanabe if and only if $\min \{H_{1}K_1,H_{2}K_2\}<{1}/{(d+2)}$.
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