The derivative of self-intersection local time of various stochastic processes

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.