The aim of this project is to become familiar with two of the main concepts in probability theory, namely Markov processes and martingales. Our main example of both concepts will be Brownian motion in Rd. One of the main applications of the notion of martingales is its connection to partial differential equations, which leads to the study of integration with respect to stochastic processes and in turn to the study of so-called stochastic differential equations.
Book:
Ioannis Karatzas and Steven E. Shreve, Brownian motion and stochastic calculus
Term:
Spring
Year:
2016