250068 VO Stochastic Analysis (2025W)
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Language: English
Examination dates
Lecturers
Classes (iCal) - next class is marked with N
- Monday 06.10. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 09.10. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Monday 13.10. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Monday 20.10. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 23.10. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Monday 27.10. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Monday 03.11. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 06.11. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Monday 10.11. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Monday 17.11. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 20.11. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Monday 24.11. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Monday 01.12. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 04.12. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Monday 15.12. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 18.12. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Monday 12.01. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 15.01. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Monday 19.01. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Monday 26.01. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 29.01. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
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Aims, contents and method of the course
Assessment and permitted materials
Minimum requirements and assessment criteria
Examination topics
Reading list
These are modern, self-contained treatments:Jean-François Le Gall — Brownian Motion, Martingales, and Stochastic Calculus (Springer, 2016)
Modern, concise, and very clear. Starts from Gaussian spaces and constructs Brownian motion rigorously (the book you’ve already cited). Excellent for a first rigorous course.Steven E. Shreve — Stochastic Calculus for Finance II: Continuous-Time Models (Springer, 2004)
While oriented to finance, the exposition of Itô calculus is pedagogically excellent and suitable for applied mathematics lectures.Bernt Øksendal — Stochastic Differential Equations: An Introduction with Applications (Springer, 7th ed. 2013)
A popular general introduction; accessible yet rigorous enough. Covers Itô calculus, SDEs, and applications in physics and finance.The following are the standard mathematical introductions to stochastic calculus and continuous-time martingale theory.Daniel Revuz & Marc Yor — Continuous Martingales and Brownian Motion (Springer, 3rd ed. 1999)
The canonical advanced reference. Very thorough, technically demanding, and beautifully written. Best for mathematically mature students after they already know basic probability.
Topics: Brownian motion, local time, stochastic integrals, Itô’s formula, Girsanov theorem, excursions.Kiyosi Itô & Henry McKean — Diffusion Processes and Their Sample Paths (Springer, 1965/1996 reprint)
Historical but foundational — rigorous introduction to diffusion processes and SDEs from the original sources.L. C. G. Rogers & David Williams — Diffusions, Markov Processes and Martingales (2 vols., Cambridge University Press, 2nd ed. 2000)
Volume 1: basic theory of Markov processes and martingales.
Volume 2: Itô calculus, stochastic integration, and applications.
Clear, complete, and widely used in research training.
Modern, concise, and very clear. Starts from Gaussian spaces and constructs Brownian motion rigorously (the book you’ve already cited). Excellent for a first rigorous course.Steven E. Shreve — Stochastic Calculus for Finance II: Continuous-Time Models (Springer, 2004)
While oriented to finance, the exposition of Itô calculus is pedagogically excellent and suitable for applied mathematics lectures.Bernt Øksendal — Stochastic Differential Equations: An Introduction with Applications (Springer, 7th ed. 2013)
A popular general introduction; accessible yet rigorous enough. Covers Itô calculus, SDEs, and applications in physics and finance.The following are the standard mathematical introductions to stochastic calculus and continuous-time martingale theory.Daniel Revuz & Marc Yor — Continuous Martingales and Brownian Motion (Springer, 3rd ed. 1999)
The canonical advanced reference. Very thorough, technically demanding, and beautifully written. Best for mathematically mature students after they already know basic probability.
Topics: Brownian motion, local time, stochastic integrals, Itô’s formula, Girsanov theorem, excursions.Kiyosi Itô & Henry McKean — Diffusion Processes and Their Sample Paths (Springer, 1965/1996 reprint)
Historical but foundational — rigorous introduction to diffusion processes and SDEs from the original sources.L. C. G. Rogers & David Williams — Diffusions, Markov Processes and Martingales (2 vols., Cambridge University Press, 2nd ed. 2000)
Volume 1: basic theory of Markov processes and martingales.
Volume 2: Itô calculus, stochastic integration, and applications.
Clear, complete, and widely used in research training.
Association in the course directory
MSTV; MANV; ML2; MEL
Last modified: Tu 10.03.2026 07:27