Generalized fractional Brownian motion
Abstract
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, H\"older continuity, nondifferentiablity, and existence of a local time.
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