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) |
|---|---|
| Pages (from-to) | 550-574 |
| Number of pages | 25 |
| Journal | Journal of Theoretical Probability |
| Volume | 35 |
| Issue number | 1 |
| DOIs | |
| State | Published - Mar 2022 |
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- General Mathematics
- Statistics, Probability and Uncertainty
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