Andreas Eberle - Vorlesungen

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Stochastic Analysis, WS 2011/12

Tuesdays 12.15-14.00 and Thursdays 12.15-14.00, KHS, Wegelerstr. 10

Lecture Course: Andreas Eberle

Tutorial Classes: Evangelia Petrou, Wednesdays 16.15-18.00, 0.011 

Hand in solutions to exercises: Tuesdays before 14.00

Examination: Oral, t.b.a.

Topics to be covered: Levy processes. Stochastic integration theory for semimartingales. Stochastic Differential Equations: weak solutions and martingale problem; strong solutions and stochastic flows; numerical methods; derivative flows and Malliavin calculus.

Lecture Notes:

• The Lecture Notes Stochastic Analysis are prepared during the course and made available here. Please send corrections (including minor typos) to David Aschenbrücker.The notes Introduction to Stochastic Analysis contain the material covered in last year's Bachelor course Grundzuege der Stochastischen Analysis.

 

Material:

• Recommended Reading
• "Stochastische Differentialgleichungen, Eulerschema (Mathematica Notebook)"
• "Geometrische Brownsche Bewegung (Mathematica Notebook)"
• "Feller's branching diffusion (Mathematica Notebook)"
• "Cox-Ingersoll-Ross Modell (Mathematica Notebook)"
• "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)"

 

Exercise Sheets:

• Sheet 1 (Hand in before 18.10.)

• Sheet 2 (Hand in before 25.10.)

• Sheet 3 (Hand in before 2.11.)

• Sheet 4 (Hand in before 8.11.)

• Sheet 5 (Hand in before 15.11.)

• Sheet 6 (Hand in before 22.11.)

• Sheet 7 (Hand in before 29.11.)

• Sheet 8 (Hand in before 6.12.)

• Sheet 9 (Hand in before 13.12.)

• Sheet 10 (Hand in before 10.1./17.1.)

 

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October 2011 Andreas Eberle eberleadf@uni-bonnfdsa.de