This monograph investigates the existence and regularity properties of local times for continuous semimartingales and excursion theory for Brownian paths. The authors, Ju-Yi Yen and Marc Yor, draw upon their expertise in stochastic analysis to present a rigorous treatment of these advanced mathematical concepts. The work explores how Brownian excursion processes can be related to Wiener process realizations under specific conditions, leading to novel applications. It covers topics such as the arc sine law, laws of functionals of Brownian motion, and the Feynman-Kac formula, demonstrating the utility of these theoretical tools.

This monograph is a specialized academic text focusing on advanced topics in probability theory and stochastic processes. Its content suggests a rigorous and theoretical approach, likely appealing to researchers and graduate students in mathematics and mathematical physics. The detailed exploration of local times and excursion theory, along with its applications, indicates a work intended for those with a strong background in the field. The authors' established expertise in stochastic analysis further supports its positioning as a significant contribution to the literature.