MA 365: Topics in Gaussian Processes
Credits: 3:0
Prerequisite courses: MA 361
A course in Gaussian processes. At first we shall study basic facts about Gaussian processes - isoperimetric inequality and concentration, comparison inequalities, boundedness and continuity of Gaussian processes, Gaussian series of functions, etc. Later we specialize to smooth Gaussian processes and their nodal sets , in particular expected length and number of nodal sets, persistence probability and other such results from recent papers of many authors.
Suggested books and references:
- Robert Adler and Jonathan Taylor, Gaussian Random Fields, Springer, New York, 2007.
- Svante Janson, Gaussian Hilbert Spaces, Cambridge University Press, Cambridge, 1997.
- A. I. Bogachev, Gaussian Measures, American Mathematical Society, Providence, RI, 1998.
- Michel Ledoux and Michel Talagrand, Probability in Banach spaces. Isoperimetry and processes, Springer-Verlag, Berlin, 2011.
- Michel Ledoux, Isoperimetry and Gaussian analysis, St. Flour lecture notes-1994.