Abstract
Fractional Laplace motion is obtained by subordinating fractional Brownian motion to a gamma process. Used recently to model hydraulic conductivity fields in geophysics, it may also prove useful in modeling financial time series. Its one dimensional distributions are scale mixtures of normal laws, where the stochastic variance has the generalized gamma distribution. These one dimensional distributions are more peaked at the mode than a Gaussian, and their tails are heavier. In this paper, we derive the basic properties of the process, including a new property called stochastic self-similarity. We also study the corresponding fractional Laplace noise, which may exhibit long-range dependence. Finally, we discuss practical methods for simulation.
| Original language | English |
|---|---|
| Pages (from-to) | 451-464 |
| Journal | Advances in Applied Probability |
| Volume | 38 |
| Issue number | 2 |
| Publication status | Published - 2006 |
| Externally published | Yes |
Subject classification (UKÄ)
- Probability Theory and Statistics
Free keywords
- infinite divisibility
- generalized gamma distribution
- subordination
- gamma process
- scaling
- self-similarity
- long-range dependence
- self-affinity
- fractional Brownian motion
- Compound process
- G-type distribution