Multipower variation for Brownian semistationary processes
In this paper we study the asymptotic behaviour of power and multipower variations of processes Y: Yt = ∫−∞t g(t − s)σsW(ds) + Zt, where g : (0, ∞) → ℝ is deterministic, σ > 0 is a random process, W is the stochastic Wiener measure and Z is a stochastic process in the nature of a drift term. Proc...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
4 November 2011
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| In: |
Bernoulli
Year: 2011, Volume: 17, Issue: 4, Pages: 1159-1194 |
| ISSN: | 1573-9759 |
| DOI: | 10.3150/10-BEJ316 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.3150/10-BEJ316 Verlag, Volltext: http://projecteuclid.org/euclid.bj/1320417500 
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| Author Notes: | Ole E. Barndorff-Nielsen, José Manuel Corcuera and Mark Podolskij |
| Summary: | In this paper we study the asymptotic behaviour of power and multipower variations of processes Y: Yt = ∫−∞t g(t − s)σsW(ds) + Zt, where g : (0, ∞) → ℝ is deterministic, σ > 0 is a random process, W is the stochastic Wiener measure and Z is a stochastic process in the nature of a drift term. Processes of this type serve, in particular, to model data of velocity increments of a fluid in a turbulence regime with spot intermittency σ. The purpose of this paper is to determine the probabilistic limit behaviour of the (multi)power variations of Y as a basis for studying properties of the intermittency process σ. Notably the processes Y are in general not of the semimartingale kind and the established theory of multipower variation for semimartingales does not suffice for deriving the limit properties. As a key tool for the results, a general central limit theorem for triangular Gaussian schemes is formulated and proved. Examples and an application to the realised variance ratio are given. |
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| Item Description: | Gesehen am 29.05.2018 |
| Physical Description: | Online Resource |
| ISSN: | 1573-9759 |
| DOI: | 10.3150/10-BEJ316 |