Advanced course on Stochastic Processes for Ph.D. and MS students (Winter-Spring 2018)
This course is devoted to advanced and more recent topics in stochastic processes and fields.
Some topics to teach are as follows:
- Multivariate PDF and associated transformations
- Weighted and Un-weighted Two-Point correlation function of different features
- Master equations
- Fokker-Planck equation
- Covariant form of Fokker-Planck equation
- Topological and geometrical features of Stochastic fields
- Perturbative approach for Non-Gaussian fields
- Effective Theory for perturbations
Course subjects and program (Download)- Stochastic fields: Definition and classification (Download)
- Statistics of smoothed cosmic fields in perturbation theory I: Formulation and useful formulas in second-order perturbation theory (Download)
- Some good books are written by Adler:
1)The Geometry of Random Fields, https://doi.org/10.1137/1.9780898718980
2) Random Fields and Geometry
3) Topological Complexity of Smooth Random Functions - My note about Topological an Geometrical feature of stochastic fields (Download)
- A good text for commands in Fortran, C++, Matlab (Download)
- VPython
- Some necessary things for programming skills (Download)
- Online numerical recipes (http://www.nr.com)
- My lecture concerning Errors and PDF (Download) (Download)
- Some of my Python programs (Download)
- Visualization by Matlab (link)
- Discretization approaches (Download)
Mid-term with answer-key: (Download)
| ش دانشجویی | midterm/60 |
| 96516002 | 28 |
| 96416013 | 30.5 |
| 96416049 | 45 |
| 96416052 | 33.5 |
| 96516014 | 36 |
| 96416087 | 11.5 |
| 96416090 | 23 |
| 96416091 | غایب |
Exercises: Thanks to Mr. Kargaran and Ms. Bagheri to provide answer key
# Set 1 (Download) data (Download) ************ Answer key set 1 (Download)
# Set 2 (Download) *************************** Answer key set 2 (Download)
# Set 3 (Download) data (Download) ************* Answer key set 3 (Download)
# Set 4 (Download) *************************** Answer key set 4 (Download)
# Set 5 (Download) *************************** Answer key set 5 (Download)
# Set 6 (Download) *************************** Answer key set 6 (Download)
# Set 7 (Download) *************************** Answer key set 7 (Download)