Strassen泛函LIL的推广
A generalization of Strassen's functional LIL
摘要：
设X_1，X_2，. . .是一个i.i.d.序列。平均为零随机变量，令S_n为前n个随机变量之和。证明了当lim sup_n |S_n| /c_n以概率1有限且正规化序列{c_n}充分正则时，对应的正规化部分和过程序列在C[0，1]中具有规范聚值集是相对紧的.将此结果与无穷方差情形下的LIL型结果相结合，得到了该情形下的Strassen型结果。
英文摘要：
Let X_1,X_2, . . . be a sequence of i.i.d. mean zero random variables and let S_n the sum of the first n random variables. We show that whenever lim sup_n |S_n|/c_n is finite with probability one and the normalizing sequence {c_n} is sufficiently regular, the corresponding normalized partial sum process sequence is relatively compact in C[0, 1] with canonical cluster set. Combining this result with some LIL type results in the infinite variance case, we obtain Strassen type results in this setting.
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