Introduction to Stochastic Analysis, WS 2015/16

Tuesday 8.30-10.00 and Friday 10.15-12.00, Zeichensaal, Wegelerstr. 10

Lecture Course: Matthias Erbar

Problem sheets: Lorenzo Dello Schiavo

 

Tutorials

Mo 8-10, 0.008, Felix Wolf

Mo 10-12, 0.007, Maximilian Fels

Th 12-14, 0.007, Victor Erpenbeck

Please hand in your solutions tuesdays during the lecture.

 

Exam

oral examination; the examination will be in groups of two.

Dates: first round February 20, 21, 22; second round March 20.

Contents

• martingales in discrete and continuous time
• Brownian motion
• continuous semimartingales
• stochastic integration
• Ito formula and applications
• stochastic differential equations

 

Reference material

• D. Williams : Probability with martingales, Cambridge UP
• I. Karatzas, S. Shreve : Brownian motion and stochastic calculus, Springer
• M. Steele : Stochastic calculus and financial applications, Springer
• Lecture notes of Andreas Eberle: Introduction to stochastic Analysis
• D. Revuz, M. Yor: Continuous martingales and Brownian motion, Springer
• Rogers, Williams : Diffusions, Markov processes and martingales, Cambridge UP
• Durrett : Stochastic calculus, CRC Press
• Klenke: Wahrscheinlichkeitstheorie, Springer