Shahid Beheshti University

Department of Physics

  • Increase font size
  • Default font size
  • Decrease font size

Stochastic Processes (Winter-Spring 2021)

E-mail Print

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 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

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

 

Some of my lectures on the Board

Midterm exam:  (Download) 1400/02/09 ,  Answer-key (Download)

Final exam:

 

Exercises:                           

# Set 1 (Download) data (Download)

# Set 2 (Download)

# Set 3 (Download) data (Download)

# Set 4 (Download)

# Set 5 (Download) data (Download)

# Set 6 (Download) data1 (Download) data (including 0.2.txt, 0.5.txt and 0.8.txt) (Download)

# Set 7 (Download)

# Set 8 (Download)

# Set 9 (Download)

# Set 10 (Download)

# Set 11 (Download)

# Set 12 (Download)

# Set 13 (Download)

Last Updated on Tuesday, 01 June 2021 11:01  


Search