Introduction to Interacting Diffusions

Interacting particle systems is a growing field of probability theory that is devoted to the rigorous analysis of certain types of models involving a large number of interrelated components. These models arise in statistical physics, biology, economics, and other fields. In this dissertation we aim at studying systems of interacting particles using stochastic differential equations. In particular we are interested in the limit when the number n of particles is sent to infinity. This study will lead us to introduce and study the so-called McKean-Vlasov equation.