n重分数布朗运动的Strassen泛函重对数律

Strassen’s Functional LIL for n-times Iterated Fractional Brownian Motion

本文给出了由两个不同的分数布朗运动组成的重分数布朗运动的Strassen型泛函重对数律和局部Strassen型泛函重对数律.我们的结果也适用于由两个布朗运动组成的重布朗运动及由一个分数布朗运动和一个布朗运动组成的重过程.最后将上述结果推广到n重分数布朗运动中.推广了已有文献的相应结果.

In this paper,we present a Strassen-type functional law of the iterated logarithm(LIL for short) and a local functional LIL of the iterated fractional Brownian motion composed of two different fractional Brownian motions.Our results also hold for the iterated Brownian motion composed of two Brownian motions and the iterated process composed of one fractional Brownian motion and one Brownian motion.Finally,we extend the above results to the case of n-times iterated fractional Brownian motion.The corresponding results of existing literature are extended.