Path Properties of a Generalized Fractional Brownian Motion
Abstract
The generalized fractional Brownian motion is a Gaussian self-similar process whose increments are not necessarily stationary. It appears in applications as the scaling limit of a shot noise process with a power law shape function and non-stationary noises with a power-law variance function. In this paper we study sample path properties of the generalized fractional Brownian motion, including Holder continuity, path differentiability/non-differentiability, and functional and local Law of the Iterated Logarithms.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2020
- DOI:
- 10.48550/arXiv.2009.07788
- arXiv:
- arXiv:2009.07788
- Bibcode:
- 2020arXiv200907788I
- Keywords:
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- Mathematics - Probability