Welcome to the “Stochastic Processes” (CE-40695) course! This is a graduate level course that aims to provide a fundamental understanding of stochastic processes for computer science students.

### Main References of the Course

- Robert G. Gallager, “Stochastic Processes: Theory for Applications,” Cambridge University Press, 1st edition, Feb., 2014.
- Athanasios Papoulis and S. Unnikrishna Pillai, “Probability, Random Variables and Stochastic Processes,” McGraw-Hill Europe, 4th edition, Jan., 2002.
- George Casella and Roger L. Berger, “Statistical Inference,” Wadsworth Press, 2nd edition, Jun., 2001.

### Sample Simulation Codes

Having access to computers and programming languages that can produce (though approximately) many random variables, it is a great opportunity that many aspects of stochastic processes can be show by writing simulation programs. In this page, I will gradually add more simulations that help students to have a better understanding of many stochastic processes concepts.

## Spring 2021 Lectures

In the following, the lecture videos and notes of spring 2021 semester can be found (the lectures and notes are in Persian).

# | Date | Subject | Video | Note |

1 | 1399-11-25 | Introduction to probability: Axioms of probability theory, Random variables | Lec 1 | Note 1 |

2 | 1399-11-27 | Introduction to probability: Random variables, Expected value, Moments of a random variable | Lec 2 | Note 2 |

3 | 1399-12-02 | Introduction to probability: Moment generating function, Some probabilistic inequalities | Lec 3 | Note 3 |

4 | 1399-12-04 | Introduction to probability: Law of large number, Central limit theorem, Convergence of random variables | Lec 4 | Note 4 |

5 | 1399-12-09 | Introduction to stochastic processes: Basic definitions, Statistical properties of stochastic processes | Lec 5 | Note 5 |

6 | 1399-12-11 | Introduction to stochastic processes: Statistical properties of stochastic processes, Stationary processes | Lec6 | Note 6 |

7 | 1399-12-16 | Introduction to stochastic processes: Stationary processes, Periodic processes | Lec 7 | Note 7 |

8 | 1399-12-18 | Introduction to stochastic processes: Ergodicity | Lec 8 | Note 8 |

9 | 1399-12-23 | Introduction to stochastic processes: Ergodicity, Systems with random input | Lec 9 | Note 9 |

10 | 1400-01-14 | Introduction to stochastic processes: Systems with random input, Power spectrum | Lec 10 | Note 10 |

11 | 1400-01-16 | Poisson processes: Arrival and renewal processes, Memoryless property, Definition and properties of a Poisson process | Lec 11 | Note 11 |

12 | 1400-01-21 | Poisson processes: Properties of a Poisson process | Lec 12 | Note 12 |

13 | 1400-01-23 | Poisson processes: Other definitions of a Poisson process, Combining and splitting Poisson processes | Lec 13 | Note 13 |

14 | 1400-01-28 | Gaussian processes: Gaussian random variables and random vectors, Jointly-Gaussian random vectors | Lec 14 | Note 14 |

15 | 1400-01-30 | Gaussian processes: Generating functions of Gaussian random vectors, Gaussian processes | Lec 15 | Note 15 |

16 | 1400-02-04 | Finite-state Markov chains: Representations of a Markov chain, Classification of states | Lec 16 | Note 16 |

17 | 1400-02-06 | Finite-state Markov chains: Classification of states, Matrix representation, Steady state | Lec 17 | Note 17 |

18 | 1400-02-11 | Finite-state Markov chains: Matrix representation, Steady state, Steady state assuming P>0 | Lec 18 | Note 18 |

19 | 1400-02-13 | Finite-state Markov chains: Steady state assuming P>0, Steady state for ergodic Markov chains and unichains | Lec 19 | Note 19 |

20 | 1400-02-18 | Finite-state Markov chains: Steady state for Markov chain with two states | Lec 20 | Note 20 |

21 | 1400-02-25 | Finite-state Markov chains: Steady state for arbitrary Markov chains — Estimation theory: Statistics, sufficiency principle, and sufficient statistic | Lec 21 | Note 21 |

22 | 1400-02-27 | Estimation theory: Sufficient statistic, Factorization theorem | Lec 22 | Note 22 |

23 | 1400-03-01 | Estimation theory: Minimal sufficient statistic | Lec 23 | Note 23 |

24 | 1400-03-08 | Estimation theory: The likelihood principle — Point estimation: Methods of finding estimators, Method of moments | Lec 24 | Note 24 |

25 | 1400-03-10 | Point estimation: Maximum likelihood estimators | Lec 25 | Note 25 |

26 | 1400-03-17 | Point estimation: Bayes estimators, Methods of evaluating estimators, Mean squared error | Lec 26 | Note 26 |

27 | 1400-03-25 | Point estimation: Best unbiased estimators | Lec 27 | Note 27 |