Advanced course on Stochastic Processes for Ph.D. and MS students (Winter-Spring 2022)
This course is devoted to advanced and more recent topics in stochastic processes and fields.
Link for class https://vc15.sbu.ac.ir/class-4002161820601/
Link for my previous lectures on Computational Physics (VPN needed)
Link for my previous lectures on Optimization (VPN needed)
Link for my previous lectures on Stochastic Processes (2021) (VPN needed)
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)
- A good movie presented by Pooyan Goodarzi to connect the server, remotely (Link)
- 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
My previous lectures (Link)
My lectures on the board
- Preliminary part (Download)
- Data Science (Download)
- Error estimation (error estimation) my note included (error estimation)
- 991129 (comp981213), (comp981215) & (comp981218)
- See also my lecture presented in school on statistical analysis of cosmological random fields
- A good paper for correlations , Marti, Gautier, et al. "A review of two decades of correlations, hierarchies, networks and clustering in financial markets." Progress in Information Geometry (2021): 245-274.
Midterm exam: The midterm will be held on 25 Farvardin 1401 at 9:00 am (Changed to 8 Ordibehesht 1401 at 9:00 am)
Final exam with answer-key: (Download)
Marks (Download)
Exercises:
# Set 1 (Download) data (Download)
# Set 2 (Download)
# Set 3 (Download)
# Set 4 (Download) Data (Download)
# Set 5 (Download) data1 (Download) data (including 0.2.txt, 0.5.txt and 0.8.txt) (Download)
# Set 6 (Download)
# Set 7 (Download)
# Set 8 (Download) Based on the paper PRE, 72, 046220 (2005) "Visualization of coupling in time series by order recurrence plots", Data (Download)
# Set 9 (Download)
# Set 10 (Download)
# Set 11 (Download)
# Set 12 (Download) data (including 0.2.txt, 0.5.txt and 0.8.txt) (Download) and some complementary references (Link) & (Download)
