On pathwise quadratic variation for càdlàg functions

Electronic Communications in Probability

Henry Chiu¹ 

关键词: quadratic variation;    semimartingale;    pathwise calculus;    Ito formula;    pathwise integration;    cadlag functions;    Skorokhod topology;   

DOI  :  10.1214/18-ECP186

学科分类：统计和概率

来源: Institute of Mathematical Statistics

【 摘 要 】

We revisit Föllmer’s concept of quadratic variation of a càdlàg function along a sequence of time partitions and discuss its relation with the Skorokhod topology. We show that in order to obtain a robust notion of pathwise quadratic variation applicable to sample paths of càdlàg processes, one must reformulate the definition of pathwise quadratic variation as a limit in Skorokhod topology of discrete approximations along the partition. One then obtains a simpler definition which implies the Lebesgue decomposition of the pathwise quadratic variation as a result, rather than requiring it as an extra condition.

【 授权许可】

CC BY