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Stochastic Differential Equations (TU+)
| Credits |
6 credit points |
| Instructors |
Weide, J.A.M. van der (Technische Universiteit Delft), Bagchi, A. (Universiteit Twente), Neerven, J.M.A.M. van (Technische Universiteit Delft), Wittich, Olaf (Technische Universiteit Eindhoven) |
| E-mail |
J.A.M.vanderWeide@EWI.TUDelft.NL, a.bagchi@ewi.utwente.nl, J.M.A.M.vanNeerven@TUDelft.nl, o.wittich@tue.nl |
| Description |
After a brief survey of some basic results from Measure Theory and Probability Theory, the concept of a martingale is introduced and studied, first in discrete time and then in continuous time. The main example in continuous time is the Brownian motion process. After these preparations we turn to the development of the Itô stochastic calculus. The Itô isometry and the Itô ormula are derived. The theory is applied to obtain solutions of certain classes of stochastic differential equations. We conclude with a brief introduction to the theory of diffusions. |
| Examination |
Written exam. |
| Literature |
J. M. Steele, 'Stochastic Calculus and Financial Applications', Springer, 2001. |
| Prerequisites |
Analysis, Probability and Stochastic Processes. |
| Remarks |
This course offers the background needed for advanced courses in Stochastic Analysis, Statistics, Mathematical Finance, and Functional Analysis. This course is part of the 3TU Mathematics Electives. Course website http://www.win.tue.nl/~wittich/ |
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