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Abstract

Hermite variations are variants of the p-variations of stochastic processes, involving the Hermite polynomials applied to the increment of the process under analysis. This type of variations fits well into Malliavin calculus context. We discuss in this chapter the limit behavior in distribution of the Hermite variations of the fractional Brownian motion, fractional Brownian sheet and moving—average sequences. The chapter also presents Hsu-Robbins and Spitzer theorems corresponding to the limit behavior in distribution of the Hermite variations.

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Tudor, C.A. (2013). Hermite Variations for Self-similar Processes. In: Analysis of Variations for Self-similar Processes. Probability and Its Applications. Springer, Cham. https://doi.org/10.1007/978-3-319-00936-0_6

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