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http://hdl.handle.net/2445/23393
Title: | Multipower variation for Brownian semistationary processes |
Author: | Barndorff-Nielsen, O. E. (Ole E.) Corcuera Valverde, José Manuel Podolskij, Mark |
Keywords: | Processos de moviment brownià Teorema del límit central Processos gaussians Brownian motion processes Central limit theorem Gaussian processes |
Issue Date: | 2011 |
Publisher: | Bernoulli Society for Mathematical Statistics and Probability |
Abstract: | In this paper we study the asymptotic behaviour of power and multipower variations of processes Y : Yt = Z t 1 g(t s) sW (ds) +Zt In this paper we study the asymptotic behaviour of power and multipower variations of processes $Y$:\[Y_t=\int_{-\in fty}^tg(t-s)\sigma_sW(\mathrm{d}s)+Z_t,\] where $g:(0,\infty)\rightarrow\mathbb{R}$ is deterministic, $\sigma >0$ 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 $\sigma$. 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 $\sigma$. 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. |
Note: | Reproducció del document publicat a: http://dx.doi.org/10.3150/10-BEJ316 |
It is part of: | Bernoulli, 2011, vol. 17, núm. 4, p. 1159-1194 |
URI: | http://hdl.handle.net/2445/23393 |
Related resource: | http://dx.doi.org/10.3150/10-BEJ316 |
ISSN: | 1350-7265 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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