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See detailAsymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian-fractional Brownian model
Azmoodeh, Ehsan UL; Sottinen, Tommi; Viitasaari, Lauri

in Modern Stochastics: Theory and Applications (2015), 2(1), 2949

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See detailNecessary and sufficient conditions for Hölder continuity of Gaussian processes
Azmoodeh, Ehsan UL; Sottinen, Tommi; Viitasaari, Lauri et al

in Statistics and Probability Letters (2014), 94

The continuity of Gaussian processes is an extensively studied topic and it culminates in Talagrand’s notion of majorizing measures that gives complicated necessary and sufficient conditions. In this note ... [more ▼]

The continuity of Gaussian processes is an extensively studied topic and it culminates in Talagrand’s notion of majorizing measures that gives complicated necessary and sufficient conditions. In this note we study the Hölder continuity of Gaussian processes. It turns out that necessary and sufficient conditions can be stated in a simple form that is a variant of the celebrated Kolmogorov–Čentsov condition. [less ▲]

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See detailAsymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian-fractional Brownian model
Azmoodeh, Ehsan UL; Sottinen, Tommi; Viitasaari, Lauri

E-print/Working paper (2014)

We study asymptotic normality of the randomized periodogram estimator of quadratic variation in the mixed Brownian--fractional Brownian model. In the semimartingale case, that is, where the Hurst ... [more ▼]

We study asymptotic normality of the randomized periodogram estimator of quadratic variation in the mixed Brownian--fractional Brownian model. In the semimartingale case, that is, where the Hurst parameter H of the fractional part satisfies H∈(3/4,1), the central limit theorem holds. In the nonsemimartingale case, that is, where H∈(1/2,3/4], the convergence toward the normal distribution with a nonzero mean still holds if H=3/4, whereas for the other values, that is, H∈(1/2,3/4), the central convergence does not take place. We also provide Berry--Esseen estimates for the estimator. [less ▲]

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