Essentials of Brownian Motion and Diffusion

The book aims to develop the topic of what is loosely called Brownian motion and diffusion theory in such a way as to make the fundamentals accessible to a nonspecialist in the field and to provide a sound basic grasp of the subject without going into the most refined of the technicalities. The intent has been to select and emphasize those results which either have an immediate observational meaning or which seem to contribute most to a general understanding of the subject. The first part of the book presents general properties of the Brownian motion, including the definition, probabilistic and analytic properties, general Markov methods, generalizations, and applications. The second part contains the study of local times (in particular, the Trotter theorem) and various types of boundary conditions for Brownian motion.