Necessary and sufficient condition for the smoothness of intersection local time of subfractional Brownian motions

作者：Shen, Guangjun^*

来源：JOURNAL OF INEQUALITIES AND APPLICATIONS, 2011, 2011(1): 139.

DOI：10.1186/1029-242X-2011-139

• subfractional Brownian motion
• intersection local time
• Chaos expansion

Let S-H and (S) over tilde (H) be two independent d-dimensional sub-fractional Brownian motions with indices H is an element of (0, 1). Assume d >= 2, we investigate the intersection local time of subfractional Brownian motions
l(T) = (T)integral(0) (T)integral(0) delta (S-t(H) - (S) over tilde (H)(s)) dsdt, T > 0,
where delta denotes the Dirac delta function at zero. By elementary inequalities, we show that l T exists in L-2 if and only if Hd <2 and it is smooth in the sense of the Meyer-Watanabe if and only if H < 2/d+2. As a related problem, we give also the regularity of the intersection local time process.

• 出版日期2011
• 单位安徽师范大学