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First and Second Order Quadratic Variations. Wavelet-Type Variations

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Analysis of Variations for Self-similar Processes

Part of the book series: Probability and Its Applications ((PIA))

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Abstract

In this chapter we study the asymptotic behavior of the quadratic variation (including standard quadratic, quadratic variation based on higher order increments or wavelet-type quadratic variations) for several self-similar processes, such as fractional Brownian motion, the Rosenblatt process, the Hermite process of general order or the solution to the linear heat equation. We prove Central or Non-Central Limit Theorems for the sequence of quadratic variations using chaos expansion into multiple Wiener-Itô integrals and Malliavin calculus.

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  1. UFR Mathématiques, Université de Lille 1, Villeneuve d’Ascq, France

    Ciprian A. Tudor

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Tudor, C.A. (2013). First and Second Order Quadratic Variations. Wavelet-Type Variations. In: Analysis of Variations for Self-similar Processes. Probability and Its Applications. Springer, Cham. https://doi.org/10.1007/978-3-319-00936-0_5

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