Abstract:

Let B^{H, K}={B^{H, K}(t), t ≥ 0 } be a bifractional Brownian motion in R^d with Hurst indexes H ∈ (0, 1) and K ∈ (0, 1]. This process constitutes a natural generalization of fractional Brownian motion(which is obtained for K=1). In this paper, we research the smoothness of the renormalized self-intersection local time of B^{H, K}. By the chaos expansion method of Malliavin analysis, we obtain the smoothness of the renormalized self-intersection local time of B^{H, K} in the sense of Meyer-Watanabe. And our result generalizes that of fractional Brownian motion.

Key words: Bifractional Brownian motion, Renormalized self-intersection local time, Chaos expansion, Smoothness