Level crossings of the fractional Brownian motion
Event details
| Date | 14.03.2023 |
| Hour | 15:00 › 15:50 |
| Speaker | Toyomu Matsuda (Free University) |
| Location | |
| Category | Conferences - Seminars |
| Event Language | English |
Abstract:
Studying level crossings of Gaussian processes is a classical topic of the probability theory. Yet, for rough Gaussian processes, such study is essentially restricted to the Brownian setting.
I will report progress in joint work with P. Das, R. Lochowski and N. Perkowski, where we consider level crossings of the fractional Brownian motion. Our main result is that the number of epsilon-level crossings at 0, after appropriate normalisation, converges to the local time at 0 multiplied by some constant c_H. Our key tool is the shifted stochastic sewing, recently obtained by Perkowski and the speaker. I will also report an interesting conjecture on the constant c_H, which seems to capture non-Markovianity of the fractional Brownian motion.
Practical information
- General public
- Free