The derivative of self-intersection local time of various stochastic processes
Abstract
In this thesis, we investigate the exponential integrability of the derivative of self-intersection local time for Brownian motion and symmetric $\alpha$-stable processes, employing Le Gall’s method. Using the property of local nondeterminism of Gaussian processes, we extend this study to the fractional Brownian motion case. In addition, we establish a limit theorem associated with the derivative of the self-intersection local time of fractional Brownian motion.
Fields of Study & Subjects
Stochastic processes and statistical mechanics
Stochastic processes and financial applications
Fractional Differential Equations Solutions
Publication details
- Journal / source
- Monash University
- Publication date
- 1 January 2026
- Language
- EN
- Document type
- Thesis