带跳分数维积分过程幂变差的渐近行为

Abstract

Abstract:

In this paper, we investigate asymptotic properties for realized power variations of a process given by =∫^t₀Φ_sdB^H_s+ξ_t, where B^H is a fractional Brownian motion with Hurst parameter H∈ (0,1), Φ is a process having finite q-th variation with q<1/(1-H), and ξ is a purely non-Gaussian L\'{e}vy process and is independent of B^H. We present some central limit theorems (CLT) for the realized power variations in the situation that the exponent is 1/H. Some limit theorems on the law of large numbers and the CLTs for the realized threshold power variations are obtained as well.

Key words: Realized power variation, Realized threshold power variation, High-frequency data, Long memory, Central limit theorem

CLC Number:

60F17

LIU Guang-Ying, TANG Jia-Shan, ZHANG Xin-Sheng. Asymptotic Properties for Power Variations of Fractional Integral Processes with Jumps[J].Acta mathematica scientia,Series A, 2014, 34(4): 925-937.

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Asymptotic Properties for Power Variations of Fractional Integral Processes with Jumps

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