News
9/12: The oral exams are on Wednesday, January 13, 2016, 10-12, details were distributed by email.10/11: The first project is online and due on December 3, 10:00.
4/11: Lectures will take place Wednesday, 10-12 in MVL14 except in week 46 and week 49, where they are on Thursday, 10-12 in MVL15.
28/10: The first meeting is scheduled for Wednesday, November 4, 10:00 in MVL14
Teacher
Course coordinator: Annika LangEmail: annika.lang@chalmers.se
Office: MVL2086
Course description
The aim of this course is to give an introduction to stochastic simulation with an emphasis on the simulation of random fields, especially Gaussian random fields. Besides the simulation of random variables in general, approximations of random fields and the corresponding convergence analyses are treated.We will meet once a week for seven weeks. There will be project assignments during the course and an oral exam at the end of the course. The exact schedule will be fixed with the participants at the first meeting.
Course literature
will be updated continuously and still depends on the interest of the audience- Lecture notes on Stochastic Simulation, A. Lang, J. Potthoff
- Kolmogorov-Chentsov theorem and differentiability of random fields on manifolds, R. Andreev, A. Lang
- Fast
simulation of Gaussian random fields and Erratum: Fast simulation of Gaussian random fields, A. Lang, J. Potthoff
- Isotropic Gaussian random fields on the sphere: Regularity, fast simulation and stochastic partial differential equations, A. Lang, Ch. Schwab
Schedule
| Wednesday 4/11 10-12 MVL:14 |
Introduction Random number generation: uniform distribution, inverse transformation method |
| Thursday 12/11 10-12 MVL:15 |
Random number generation: Acceptance-Rejection, special methods for normal distribution Random fields in Euclidean space: introduction and regularity Project 1 (due 3/12, 10:00) |
| Wednesday 18/11 10-12 MVL:14 |
Random fields in Euclidean space: Regularity (example Brownian motion) Isotropic fields, covariance functions, Fourier transforms |
| Wednesday 25/11 10-12 MVL:14 |
Random fields in Euclidean space: Simulation of Gaussian random fields on cubes via FFT with algorithms and examples The unit sphere |
| Thursday 3/12 10-12 MVL:15 |
Gaussian random fields on the sphere: Introduction and properties Karhunen-Loève expansions Project 2 (due 21/12, 10:00) |
| Wednesday 9/12 10-12 MVL:14 |
Gaussian random fields on the sphere: Spectral approximations and convergence Lognormal random fields |
| Wednesday 16/12 10-12 MVL:14 |
Gaussian random fields on the sphere: Decay of the angular power spectrum vs. regularity of the covariance kernel Sample Hölder regularity and differentiability Relation of Q-Wiener processes and Gaussian random fields |