Abstract
This paper presents limit theorems for realized power variation of processes of the form X t = ∫ t0 φ s dG s + ξ t 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 Lévy 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.
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Liu, G., Tang, J. & Zhang, X. Central limit theorems for power variation of Gaussian integral processes with jumps. Sci. China Math. 57, 1671–1685 (2014). https://doi.org/10.1007/s11425-013-4736-4
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DOI: https://doi.org/10.1007/s11425-013-4736-4