Introduction
Stochastic processes (or random functions) are ubiquitous in modeling for engineering, biology and finance. This course proposes an in-depth introduction to the basic mechanisms describing those objects.
We begin by a review of generating functions for probability distributions. This will allow an elementary treatment of two very classical processes, namely the simple random walk and branching processes. Then we will introduce and analyze discrete time Markov chains. A chapter is also dedicated to continuous time Markov processes, another extremely important class of models. If time allows it, we will go back to convergences of ransdom sequences and martingales.
We begin by a review of generating functions for probability distributions. This will allow an elementary treatment of two very classical processes, namely the simple random walk and branching processes. Then we will introduce and analyze discrete time Markov chains. A chapter is also dedicated to continuous time Markov processes, another extremely important class of models. If time allows it, we will go back to convergences of ransdom sequences and martingales.
This is a vertical space
Bibliography
- Grimmett, Stirzacker: Probability and Random Processes. Oxford University Press, 2020.
This is a vertical space
Important links
Please consult the
course webpage.
Here is a link to the
course calendar.
This is a vertical space
Homework
The homework will be taken from the book.
Homeworks are usually due on Friday.
The assignments are given in the attached calendar.
Rules for the homework:
The assignments are given in the attached calendar.
Rules for the homework:
- Please resolve any error in the grading (hws and tests) WINTHIN ONE WEEK after the return of each homework and exam.
- No late homeworks are accepted.
- You are encouraged to discuss the homework problems with your classmates but all your handed-in homeworks must be your own work.
This is a vertical space
Midterms
Our Midterm 1 will be on 2/28/24, from 3:30pm to 4:30pm.
Program: Lessons 1-20 (see calendar).
This link sends you to the Spring 24 Midterm, together with Some solutions
Program: Lessons 1-20 (see calendar).
This link sends you to the Spring 24 Midterm, together with Some solutions
This is a vertical space
Final exam
Our Final will be on 4/30/24 from 9am to 10am, in BNRG B268.
Program: Lessons 21-43 (see calendar).
Program: Lessons 21-43 (see calendar).
This is a vertical space
Office hours
11:30am-1pm on Monday, on Zoom.
This is a vertical space
Syllabus
This is a vertical space
Slides (Feedback on typos appreciated)
This is a vertical space
Documents with computations (notes from lectures)
- Lesson 1
- Lesson 2
- Lesson 3
- Lesson 4
- Lesson 5
- Lesson 6
- Lesson 7
- Lesson 8
- Lesson 9
- Lesson 10
- Lesson 11
- Lesson 12
- Lesson 13
- Lesson 14
- Lesson 15
- Lesson 16
- Lesson 17
- Lesson 18
- Lesson 19
- Lesson 20
- Lesson 21
- Lesson 22
- Lesson 23
- Lesson 24
- Lesson 25
- Lesson 26
- Lesson 27
- Lesson 29
- Lesson 30
- Lesson 31
- Lesson 32
- Lesson 33
- Lesson 34
- Lesson 35
- Lesson 36
- Lesson 38
- Lesson 39
- Lesson 40
- Lesson 41
- Lesson 42
This is a vertical space