Stochastic Analysis, Summer term 2015

Tuesdays 12.15-14.00 and thursdays 12.15-14.00, Kleiner Hörsaal, Wegelerstr. 10

Lecture course: Andreas Eberle

Tutorial classes: Kaveh Bashiri

Monday 12-14, Room 0.011, Wednesday 16-18, Room 0.006

Exam: Schedule

The course will cover the following topics:

• Lévy processes and Poisson point processes; stochastic calculus for semimartingales with jumps
• Transformations and weak solutions of stochastic differential equations
• Stochastic flows, approximation schemes and variations of SDE, or
• Stochastic Analysis on function spaces

Prerequisites: Ito calculus for Brownian motion, see e.g. my lecture notes on "Introduction to Stochastic Analysis".

Lecture Notes: Lecture notes are available here. Slides on Malliavin calculus.

Further References:

• Rogers/Williams: Diffusions, Markov processes and martingales, Vol.2
• Bass: Stochastic processes
• Protter: Stochastic integration and differential equations
• Applebaum: Lévy Processes and Stochastic Calculus
• More references

Simulations (Mathematica Notebooks):

• From Random Walks to Brownian motion
• Scaling limits of Random Walks
• Stable Processes as scaling limits
• Stable Processes
  
• Normal Inverse Gaussian Processes
• SDE; Euler scheme
• Geometric Brownian motion
• Feller's branching diffusion
• Cox-Ingersoll-Ross model
  

Problem Sheets:

• Sheet 1 (hand in until 13.4.)
• Sheet 2 (hand in until 20.4./23.4.)
• Sheet 3 (hand in until 30.4.)
• Sheet 4 (hand in until 7.5.)
• Sheet 5 (hand in until 13.5.)
• Sheet 6 (hand in until 21. 5.)
• Sheet 7 (hand in until 3.6.)
• Sheet 8 (hand in until 11.6./18.6.)
• Sheet 9 (hand in until 25.6.)
• Sheet 10 (hand in until 2.7.)

 

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June 2015 Andreas Eberle eberle@uni-bonn.de