Andreas Eberle - Lecture Courses

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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 eberleadf@uni-bonnfdsa.de.

Material:

 

Recommended Reading

• "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.)

 

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October 2012 Andreas Eberle eberleadf@uni-bonnfdsa.de