Stochastic Processes

• instructor: Giovanni Pistone
• when: May-June 2015
• where: Collegio Carlo Alberto

This year the course focuses on Gaussian Processes and Gaussian Spaces.

These 10 two-hours lectures are aimed to give a self-contained basic course on Gassion distribution and Gaussian Processes and to introduce some elements of the modern Malliavin Calculus. As a first orientation, we refer to

[1] Paul Malliavin. Integration and Probability. Springer 1995.

[2] Ivan Nourdin and Giovanni Peccati. Normal Approximations with Malliavin Calculus. From Stein's Method to Universality. Cambridge University Press 2012.

Lecture notes and detailed references will be provided.

The exam is based on the evaluation of weakly individual home works followed by a short final discussion of the submitted papers.

Time table

• Week 1: May 5 and May 8, 17:00-19:00, lecture room 4: One dimensional Gaussian distribution and Gaussian space. References: [1, Sec. V.1], [2, Ch. 1]. Handout: 1-d Gaussian space
• Week 2, May 12 and May 15, 17:00-19:00, lecture room 4: Multivariate Gaussian Distribution. Handout: Multivariate Gaussian distribution
• Week 3, May 19 and May 22, 17:00-19:00, lecture room 4: General Gaussian spaces. Handout: Examples of Gaussian Processes. Slides: Wiener Process
• Week 4, May 26 and May 29, 17:00-19:00: Readings from [2]
• Week 5, Jun 3 and Jun 5, 17:00-19:00: Readings from [2]

Last modified: (2015-05-22 13:42:31 CEST)