IOANNIS KARATZAS
Department of Statistics
Columbia University

We present in these lectures, in an informal manner, the very basic ideas and results of
stochastic calculus, including its chain rule, the fundamental theorems on the representation
of martingales as stochastic integrals and on the equivalent change of probability
measure, as well as elements of stochastic differential equations. These results suffice for
a rigorous treatment of important applications, such as filtering theory, stochastic control,
and the modern theory of financial economics.