Introduction to Stochastic Analysis, WS 2014/15

Schedule	Tuesday 08-10 and Friday 10-12 (Zeichensaal)
Exercices	Assistant: Peter Nejjar (LWK 3.046)
Examination	Admission critetia: 50% of the exercices points. (The exercises are relevant for the exam). First examination schedule: here. Second examination: March 30-31: schedule here.

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, Feynman-Kac 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 h-transform is here. The part concerning reflected Brownian motion is here.