
Stochastic Differential Equations
Credits 
6 credit points 
Instructors 
Neerven, J.M.A.M. van (Technische Universiteit Delft) 
Email 
J.M.A.M.vanNeerven@TUDelft.nl 
Prerequisites 
Analysis, Measure Theory, Probability and Stochastic Processes. 
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 on May 30, 14:0017:00h. Delft, CiTG, Stevinstraat 1, room 1.98. Enschede, Zaal Carre 3D Date resit: June 24 2011, 14:0017:00. Simultaneously in Delft, Faculty TBM, Instructiezaal F and in Twente, zaal HB2B (Hal 2). 
Literature 
J. M. Steele, 'Stochastic Calculus and Financial Applications', Springer, 2001. 
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. See also the homepage for excercises etc. 
