Renormalized self-intersection local time for fractional Brownian motion
Renormalized self-intersection local time for fractional Brownian motion
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DOI：
10.1214/009117905000000017
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发表时间：
2005-05
影响因子：
2.3
通讯作者：
Yaozhong Hu;D. Nualart
中科院分区：
文献类型：
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作者：
Yaozhong Hu;D. Nualart
设BHt是一个具有Hurst参数H∈(0，1)的d维分式布朗运动.设d≥2.我们证明了重整化自交局部时L=∫T 0∫t 0δ(B H t-B H S)ds dt-E(∫T 0∫t 0δ(B H t-B H S)ds dt)在L 2中存在当且仅当H≥3 2d，r(E)L e按分布收敛于正态规律N(0，Tσ2)，e趋于零，其中L e是通过(2)定义的L的近似，当H=3/(2d)时r(E)=|loge|-1，若3/(2d)<，则r(E)=e d-3/(2H)；H.
Let B H t be a d-dimensional fractional Brownian motion with Hurst parameter H ∈ (0, 1). Assume d ≥ 2. We prove that the renormalized self-intersection local time l=∫ T 0 ∫ t 0 δ(B H t - B H s )ds dt - E(∫ T 0 ∫ t 0 δ(B H t -B H s )ds dt) exists in L 2 if and only if H H ≥ 3 2d, r(e)l e converges in distribution to a normal law N(0, Tσ 2 ), as e tends to zero, where l e is an approximation of l, defined through (2), and r(e) = |loge| -1 if H = 3/(2d), and r(e) = e d-3/(2H) if 3/(2d) < H.