多维随机过程首中时的强正相依性
ON THE STRONGLY POSITIVE DEPENDENCE OF HITTING TIMES OF MULTIDIMENSIONAL PROCESSES
摘要
研究多维随机过程ｘ（ｔ）的首中时的ＳＰＤ相依结构，拓展了Ｅｂｒａｈｉｍｉ等关于ＰＯＤ（Ｐｏｓｉｔｉｖｅｌｙ Ｏｒｔｈａｎｔ Ｄｅｐｅｎｄｅｎｔ）和作者关于 ＳＰＯＤ（Ｓｔｒｏｎｇｌｙ Ｐｏｓｉｔｉｖｅｌｙ Ｏｒｔｈａｎｔ Ｄｅｐｅｎｄｅｎｔ）的某些结果．刻划ＳＰＤ的另一特征，还给出最大无穷可分过程首中时之间的ＳＰＤ性质及其首中时向量（т１（Ｕ１）Ｔ２（Ｕ２））联合分布的下界淇中Ｕｉ是增Ｂｏｒｅｌ集，ｉ＝１，２）． The Author discuses the strongly positive dependence structure among hitting times (x) of the increasing multidimensional processes X(t), Some results obtained by Ebrahimi and Ramallingam have been extended. Also, the SPD (strong positive dependent) property among hitting times of max-i.d. processes is described, and the lower bound of the joint distribution of hitting times (where Ui: is an increasing Borel set, i = 1, 2) is given.