Asymptotic expansion of the quadratic variation of a mixed fractional Brownian motion

Ciprian A. Tudor and Nakahiro Yoshida ()
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Ciprian A. Tudor: Université de Lille 1
Nakahiro Yoshida: University of Tokyo

Statistical Inference for Stochastic Processes, 2020, vol. 23, issue 2, No 9, 435-463

Abstract: Abstract We obtain the high-order asymptotic expansion for the distribution of the quadratic variation of the mixed fractional Brownian motion, which is defined as the sum of a Brownian motion and an independent fractional Brownian motion. Our approach is based on the analysis of the cumulants of this sequence. We show that both the Brownian and fractional Brownian parts contribute to the asymptotic expansion.

Keywords: Asymptotic expansion; Mixed fractional Brownian motion; Malliavin calculus; Gamma factor; Cumulant (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s11203-020-09220-6

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