Introduction to Stochastic Analysis, WS 2014/15
Schedule  Tuesday 0810 and Friday 1012 (Zeichensaal)  
Exercices  Assistant: Peter Nejjar (LWK 3.046)  
Examination 

Content
 Brownian Motion: the fil rouge of this lecture
 Martinales in discrete and continuous time
 Semimartingale
 Itô integral
 Itô formula and applications
 Transformations of the Brownian Motion: Girsanov, FeynmanKac formulas
 Stochastic differential equations (strong solutions)
References
 Book: I. Karatzas und S. Shreve, Brownian Motion and Stochastic Calculus, Springer
 Here are my scanned lecture notes of 2009 (in German). Notes written by a student during my lecture of 2012 (in English) (I did not checked them). The last part on the Doob htransform is here. The part concerning reflected Brownian motion is here.