摘要
This paper presents limit theorems for realized power variation of processes of the form Xt=t0φsdGs+ξt as the sampling frequency within a fixed interval increases to infinity.Here G is a Gaussian process with stationary increments,ξis a purely non-Gaussian L′evy process independent from G,andφis a stochastic process ensuring that the integral is well defined as a pathwise Riemann-Stieltjes integral.We obtain the central limit theorems for the case that both the continuous term and the jump term are presented simultaneously in the law of large numbers.
This paper presents limit theorems for realized power variation of processes of the form Xt = t0φsdGs ＋ ξt as the sampling frequency within a fixed interval increases to infinity. Here G is a Gaussian process with stationary increments, ξ is a purely non-Gaussian L′evy process independent from G, and φ is a stochastic process ensuring that the integral is well defined as a pathwise Riemann-Stieltjes integral. We obtain the central limit theorems for the case that both the continuous term and the jump term are presented simultaneously in the law of large numbers.
基金
supported by National Natural Science Foundation of China(Grant Nos.11071045 and 11226201)
Natural Science Foundation of Jiangsu Province of China(Grant No.BK20131340)
Social Science Foundation of Chinese Ministry of Education(Grant No.12YJCZH128)
QingLan Project ofthe Priority Academic Program Development of Jiangsu Higher Education Institutions(Auditing Science and Technology)
