  This is a guide to the mathematical theory of Brownian motion and related
stochastic processes, with indications of how this theory is related to other
branches of mathematics, most notably the classical theory of partial
differential equations associated with the Laplace and heat operators, and
various generalizations thereof. As a typical reader, we have in mind a
student, familiar with the basic concepts of probability based on measure
theory, at the level of the graduate texts of Billingsley and Durrett , and who
wants a broader perspective on the theory of Brownian motion and related
stochastic processes than can be found in these texts.
