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Applied Mathematics Course Spring 2003 |
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V. Capasso
Milan Univ. STOCHASTIC CALCULUS AND APPLICATIONS The course is intended for graduate students in Mathematics Physics, Engineering, interested in diverse applications such as biology, finance, physics, engineering, etc. As the mathematics of stochastic processes (compared to other branches) is a relatively new, yet more and more popular field in terms of research output and applications, many pure as well as applied deterministic mathematicians become interested in learning about the fundaments of stochastic theory and modern applications. The course will be delivered in a language that both of them will understand and in its content and structure will allow them to learn the essentials profoundly and in a time-efficient manner. Direct experience of applications to Biology and Finance will be discussed during the course. Purpose: The course provides an introduction to the theory of continuous-time stochastic processes. Its scope is profoundly educational of modelling real world problems wit stochastic methods. The scope is to make the attendants become critically aware of the concepts involved in current applied literature, providing them with a firm foundation of the relevant rigorous mathematical concept and techniques. Prerequisites: previous exposure to probability, even though helpful, is not essential. A background in PDE's and /or measure theory may help much more. Bibliography: -Oksendal, Stochastic Differential Equations, 1998, Springer -Friedman, Stochastic Differential Equations, 1975, AP -Meyer, Continuous Stochastic Calculus with Applications to Finance, 2001, ChapmanHall -Karatzas, Shreve, Brownian Motion and Stochastic Calculus, 1991, Springer -Embrechts, Mikosch, Kluppelberg, Modelling Extremal Events, 1997, Springer -Rolski, Schmidli, Schmidt, Teugels, Stochastic Processes for Insurance and Finance, 1998, Wiley |