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 Hölder continuity, path differentiability/non-differentiability, and functional and local law of the iterated logarithms.
Original language | English (US) |
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Journal | Journal of Theoretical Probability |
DOIs | |
State | Accepted/In press - 2021 |
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Mathematics(all)
- Statistics, Probability and Uncertainty