Modern Stochastics: Theory and Applications (Jan 2017)

Generalized fractional Brownian motion

  • Mounir Zili

DOI
https://doi.org/10.15559/16-VMSTA71
Journal volume & issue
Vol. 4, no. 1
pp. 15 – 24

Abstract

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We introduce a new Gaussian process, a generalization of both fractional and subfractional Brownian motions, which could serve as a good model for a larger class of natural phenomena. We study its main stochastic properties and some increments characteristics. As an application, we deduce the properties of nonsemimartingality, Hölder continuity, nondifferentiablity, and existence of a local time.

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