Advanced stochastic analysis

Summary

This course will give you in-depth knowledge in some topics of modern stochastic analysis. We will start with a general introduction to Gaussian measure theory followed by an introduction to Malliavin calculus and a selection of advanced topics.

Content

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Keywords

Stochastic analysis, Gaussian measures, diffusions, Wick products, Malliavin calculus

Learning Prerequisites

Required courses

Analysis I-IV

Probability

Recommended courses

Measures and integration

Probability Theory

Functional Analysis I-II

Important concepts to start the course

Basic concepts in probability theory

Basic functional analysis

Teaching methods

Weekly lectures (on blackboard) and exercise sessions with assistant

Expected student activities

Attending the lectures and solving the exercises

Assessment methods

Oral exam

Supervision

Office hours	No
Assistants	Yes
Forum	No

Resources

Virtual desktop infrastructure (VDI)

No

Bibliography

D. NUALART. The Malliavin Calculus and Related Topics, Springer, 2006.

V. I. BOGACHEV. Gaussian measures, vol. 62 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 1998.

P. BILLINGSLEY. Convergence of probability measures. John Wiley & Sons Inc., New York, 1968.

Notes/Handbook

The lecture will mainly follow the notes available at https://www.hairer.org/notes/Malliavin.pdf. They will be updated on a regular basis.

Moodle Link

• https://go.epfl.ch/MATH-525