Andreas Eberle - Lecture Courses
Stochastic Analysis, WS 2012/13
Tuesdays 12.15-14.00 KHS and Fridays 8.30-10.00, 1.007 (CHANGED !!!)
Lecture Course: Andreas EberleTutorial Classes: Sebastian Andres, Fridays 16.15-18.00 (CHANGED !!!) Hand in solutions to exercises: Tuesdays before 12.15Examination: Oral, t.b.a.
Topics to be covered: Stochastic integration theory for continuous and discontinuous semimartingales. Stochastic Differential Equations: weak solutions and martingale problem; strong solutions and stochastic flows; numerical methods; derivative flows and Malliavin calculus.
- The course will roughly follow the notes of last years' course, see Stochastic Analysis. However, I plan to focus less on Levy processes, and to include some additional material on numerical methods and Malliavin calculus instead. A solid background on Brownian Motion and Martingale Theory will be assumed. Students without such a background are recommended to attend the course Foundations in Stochastic Analysis, seeIntroduction to Stochastic Analysis for the material covered in this course.
Lecture Notes:
- The lecture notes Stochastic Analysis 2012/13 are updated constantly during the course. Please report any typos (also small ones) to eberle@uni-bonn.de.
Material:
- "Vom Random Walk zur Brownschen Bewegung (Mathematica Notebook)"
- "Scaling limits of Random Walks (Mathematica Notebook)"
- "Stable Processes (Mathematica Demonstration)"
- "Variance Gamma Process (Mathematica Demonstration)"
- "Inverse Gaussian Processes (Mathematica Demonstration)"
- "Stochastische Differentialgleichungen, Eulerschema (Mathematica Notebook)"
- "Geometrische Brownsche Bewegung (Mathematica Notebook)"
- "Feller's branching diffusion (Mathematica Notebook)"
- "Cox-Ingersoll-Ross Modell (Mathematica Notebook)"
Exercise Sheets:
Sheet 1 (Hand in before 16.10.)
Sheet 2 (Hand in before 23.10.)
Sheet 3 (Hand in before 30.10.)
Sheet 4 (Hand in before 6.11.)
Sheet 5 (Hand in before 13.11.)
Sheet 6 (Hand in before 20.11.)
Sheet 7 (Hand in before 22.11.)
Sheet 8 (Hand in before 4.12.)
Sheet 9 (Hand in before 11.12.)
Sheet 10 (Hand in before 8.1.)
Sheet 11 (Hand in before 15.1.)
Sheet 12 (Hand in before 22.1.)
October 2012 Andreas Eberle eberle@uni-bonn.de