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

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Abstract

Chapter 1 surveys the basic properties of fractional Brownian motion and related processes. Fractional Brownian motion is the only Gaussian self-similar process with stationary increments. Its applications to various area are now widely recognized. Recently, other Gaussian self-similar processes, connected with the fractional Brownian motion (the bifractional Brownian motion, the subfractional Brownian motion etc.), have been the object of the study in the scientific literature. We discuss the properties of these processes, including the regularity of their sample paths, the stochastic integral representation, the long-range dependence or the existence of their quadratic variations. We also analyze their interconnections.

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Tudor, C.A. (2013). Fractional Brownian Motion and Related 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_1

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