Stochastic Calculus

Catalog description

This course is an introductory account of the mathematical analysis of stochastic processes, i.e. systems which change in accordance with probabilistic laws. It will satisfy interests of statisticians, applied mathematicians and physicists interested in methods of solving particular problems, rather than of pure mathematicians interested in general theorems. To stress the variety of applications for the theory students will include illustrations from a number of scientific fields including financial applications, in particular Black-Scholes model of a financial market. Students will keep the mathematical techniques as elementary as possible, but a good knowledge of elementary probability theory, matrix algebra and advanced calculus is essential. Students will also include several examples of constructing models, solving problems by simulations, and statistical analysis of data from real stochastic processes.