http://www.maikonline.com/maik/download.do?uid=VAHMSOA8ZQ&ptype=401&dtype=pdf

ISSN 0898-5111, Chinese Journal of Contemporary Mathematics, 2013, Vol. 34, No. 3, pp. 201–216. Allerton Press, Inc.

Limit Theorems of Power Variation for Time-Changed Stable Levy Processes

ZHANG Shibin1 and LIN Zhengyan2

1 Corresponding author. Department of Mathematics, Shanghai Maritime University, Shanghai 201306, China. E-mail: sbzhang@shmtu.edu.cn

2 Department of Mathematics, Zhejiang University, Hangzhou 310027, China.E-mail: zlin@zju.edu.cn

Received September 16, 2012; in final form, January 8, 2013

Abstract-This paper is concerned with the asymptotic behavior of the realized power variation for

time-changed α-stable Levy processes. The authors prove a law of large numbers, which is the

uniform convergence in probability of the realized power variation after normalization. The authors also exhibit the central limit theorems of the realized power variation in all the orders exceptα=2 .

2000 Mathematics Subject Classification: 60F17, 60G17

DOI: 10.3103/S0898511113030010

Keywords: Time-Changed Levy process, Stable process, Power variation, Central limit theorem

http://www.maikonline.com/maik/download.do?uid=VAHMSOA8ZQ&ptype=401&dtype=pdf