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�� $\100dpi \inline $S^{H_i}=\{S^{H_i}_t,t\geq 0\}$$ ,
$\100dpi \inline $i=1,2$$ ��ָ��ֱ�Ϊ $\100dpi \inline $H_i\in(0,1)$$ ��ά�η��˶�.
��û��չ��ȵĲ��ʽ�� $\100dpi \inline $S^{H_1}$$ �� $\100dpi \inline $S^{H_2}$$ ��ֲ�ʱ��ཻ�ֲ�ʱ��,
�⻬�Եĳ�ֱ�Ҫ��.

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�ؼ�� �� η��˶�, ��ֲ�ʱ, �ཻ�ֲ�ʱ, ��չ��.

Abstract��

Let $\100dpi \inline $S^{H_i}=\{S^{H_i}_t,t\geq 0\}$$ , $\100dpi \inline $i=1,2$$ be two independent,
$\100dpi \inline $d$$ -dimensional sub-fractional Brownian motions with respective indices $\100dpi \inline $H_i\in(0,1)$$ .
Assume $\100dpi \inline $d\geq 2$$ . Our principal results are the necessary and sufficient condition for the
existence and smoothness of the collision local time and the intersection local time of
$\100dpi \inline $S^{H_1}$$ and $\100dpi \inline $S^{H_2}$$ through chaos expansion and elementary inequalities.

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��, ��. �η��˶��ֲ�ʱ�Ĺ⻬��[J]. Ӧ�ø��ͳ��, 2015, 31(5): 547-560. Shen Guangjun, Li Mengyu. Smoothness of the Collision Local Times of Sub-Fractional Brownian Motions. CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST, 2015, 31(5): 547-560.

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http://aps.ecnu.edu.cn/CN/ �� http://aps.ecnu.edu.cn/CN/Y2015/V31/I5/547