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Course at KTH by Prof. Yaozhong Hu
Lecturer: Prof. Yaozhong Hu
Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Canada
Host Institution: Department of Mathematics, KTH Royal Institute of Technology, Sweden
Examiner: Nacira Agram, Department of Mathematics, KTH Royal Institute of Technology
Course Description
This course offers an introduction to Malliavin calculus (stochastic calculus of variations). We develop tools on Gaussian spaces to study smoothness of distributions and densities of random variables.
Topics
Gaussian measures in finite-dimensional spaces
Hypercontractivity and logarithmic Sobolev inequality
Canonical Wiener measure and Brownian motion
Gross–Sobolev–Malliavin derivatives
Meyer’s inequality; integration by parts
Existence and smoothness of densities
Malliavin–Stein method; convergence to Gaussian and other densities
Literature
Y. Hu (2017). Analysis on Gaussian Spaces. World Scientific.
S. Watanabe (1984). Lectures on Stochastic Differential Equations and Malliavin Calculus. TIFR & Springer‑Verlag.
D. Nualart (2006). The Malliavin Calculus and Related Topics (2nd ed.). Springer.
D. Nualart (2009). Malliavin Calculus and its Applications. CBMS 110, AMS.
Examination form
The course will be examined through assignments and presentations, rather than a traditional written exam.
Students will complete a set of assignments during the course. These cover both theoretical and applied aspects of the material and must be submitted by the given deadlines.
Each student (or small group) will also prepare a short presentation on one of the assignments or a related topic, to be given at the end of the course.
The final grade will be based on:
the quality and completeness of the written assignments, and
the clarity and depth of the oral presentation.
This format is designed to encourage active participation, deeper understanding, and the development of communication skills.