Sparse stochastic processes

Course work: Each student will be asked to do a small research project inspired by the material covered in the course. The goal of these projects is to make the course material concrete by considering specific examples or by tying it to novel applications. The recommended format is to select a specific parametric family of differential operators and to then work out the details and formulas for constructing the corresponding Green’s functions, B-spline, reproducing kernel Hilbert space, Gaussian vs. sparse stochastic process, etc. 

The students will be coached for their project work, which should primarily take place during the exercise hours. Towards the end of the course, they will be asked to present their results—list of formulas, tables, and series of graphs, simulation of Gaussian vs. sparse stochastic processes—in the form of a short report/paper and presentation. Their final grade will reflect their personal involvement and the outcome of their project.