A Tutorial Introduction to Stochastic Analysis and Its Applications

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. We outline recent developments in these fields, with proofs of the major results whenever possible, and send the reader to the literature for further study.