Advanced course on Stochastic Processes for Ph.D. and MS students (Winter-Spring 2021)
This course is devoted to advanced and more recent topics in stochastic processes and fields.
Link for class https://vc15.sbu.ac.ir/class-3992161820601
Link for my previous lectures on Stochastic Processes (2021) (VPN needed)
Link for my previous lectures on Computational Physics
Some topics to teach are as follows:
- Error estimation
- Multivariate PDF and associated transformations
- Weighted and Un-weighted Two-Point correlation function of different features
- Stochastic modelling
- Master equations
- Fokker-Planck equation
- Covariant form of Fokker-Planck equation
- Topological and geometrical features of Stochastic fields
- Perturbative approach for Non-Gaussian fields
- Course subjects and program (Download)
- Stochastic fields: Preliminary part
- 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)
- My note about Topological an Geometrical feature of stochastic fields (Download)
- My lecture concerning Errors and PDF (Download) (Download)
- Data Science, my talk at Academy of Sciences 1398
- New paradigm in Scientific methods
- My course on research methods
- Modelling in Complex systems
For mathematical definition of Random Fields:
1- The Geometry of Random Fields, Robert J Adler, 1981.
2- Topological Complexity of Smooth Random Functions, Adler, Robert,Taylor, Jonathan E., Springer, 2009.
3- Geometry, Topology and Physics (Graduate Student Series in Physics) by Mikio Nakahara, 1990.
For Stochastic Processes:
4- M. Reza Rahimi Tabar, Analysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems, Using the Methods of Stochastic Processes, Springer, 2019
5- Rudolf Friedrich, Joachim Peinke, Muhammad Sahimi, M. Reza Rahimi Tabar, Physics Reports 506 162–87 (2011)
6- Risken, Hannes, Frank, Till,The Fokker-Planck Equation Methods of Solution and Applications, Springer 1996.
7- An Introduction to Stochastic Processes in Physics Kindle Edition by Don S. Lemons, 2003.
8- An Introduction to Random Vibrations, Spectral & Wavelet Analysis: Third Edition (Dover Civil and Mechanical Engineering)
9- Probability, Random Variables and Stochastic Processes 4th Edition, by Athanasios Papoulis, S. Unnikrishna Pillai, McGraw-Hill Europe; 4th edition (January 1, 2002).
10- Stochastic Modelling for Systems Biology (Chapman & Hall/CRC Mathematical and Computational Biology Book 44) 2nd Edition, Kindle Edition, by Darren J. Wilkinson, 2011.
11- Independent Component Analysis, Aapo Hyvärinen, Juha Karhunen, Erkki Oja, 2001.
12- Nonlinear Time Series Analysis 2nd Edition by Holger Kantz, 2003.
13- Brownian motion and Stochastic Calculus, 2nd Edition, Ioannis Karatzas, Steven E. Shreve, 1996.
Other related materials and courses- Researches methods course (Link)
- Critical Phenomena and Phase transitions (Link)
- Computational Physics (Link)
- Data Analysis workshop (Link)
- Data Sciences (Link)
- Challenges in training and researches in Physics (Link)
- 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)
- A good Reference for errors https://archive.org/details/TaylorJ.R.IntroductionToErrorAnalysis2ed/page/n149
Some of my lectures on the Board
- Preliminary part (Download)
- Data Science (Download)
- Error estimation (error estimation) my note included (error estimation)
- 991129 (comp981213), (comp981215) & (comp981218)
- 991205 (stochastic991205)
- 991210 (stochastic991210)
- 991212 (stochastic991212)
- 991217 (stochastic991217)
- 991219 (stochastic991219)
- 991224 (stochastic991224)
- 991226 (stochastic991226) see also (level CS), (Level Laser) and (Peak Planck)
- 000115 (stochastic000115)
- 000117 (stochastic000117)
- 000122 (stochastic000122)
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- 000129 (stochastic000129)
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- 000205 (stochastic000205)
- 000207 (stochastic000207)
- 000212 (stochastic000212)
- 000214 (stochastic000214)
- 000219 (stochastic000219)
- 000221 (stochastic000221)
- 000226 (stochastic000226)
- 000228 (stochastic000228)
- 000302 (stochastic000302)
- 000304 (stochastic000304)
- 000309 (stochastic000309)
- 000311 (stochastic000311)
Midterm exam: (Download) 1400/02/09 , Answer-key (Download)
Final exam:
Exercises:
# Set 1 (Download) data (Download)
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# Set 6 (Download) data1 (Download) data (including 0.2.txt, 0.5.txt and 0.8.txt) (Download)
# Set 7 (Download)
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# Set 13 (Download)