Abstract
Fractional Brownian motion, introduced by Benoit Mandelbrot and John Van Ness in 1968, has had a major impact on stochastic processes and their applications. We survey a few of the many developments that have stemmed from their ideas. In particular we discuss the local structure of fractional and multifractional Brownian, stable and multistable processes, emphasising the `diagonal' construction of such processes. In all this, the ubiquity and centrality of fractional Brownian motion is striking.
| Original language | English |
|---|---|
| Title of host publication | Benoit Mandelbrot - A Life in Many Dimensions |
| Editors | Michael Frame, Nathan Cohen |
| Place of Publication | Singapore |
| Publisher | World Scientific Publishing |
| Pages | 239-256 |
| Number of pages | 18 |
| ISBN (Electronic) | 978-9814366076 |
| ISBN (Print) | 978-9814366069 |
| Publication status | Published - 29 Apr 2015 |
Keywords
- Fractal, Mandelbrot