Stochastic Processes 2024

Logistics

Timings: Thursday at 2:00 PM and Friday at 9:00 AM

Teaching Assistants: Sumana A (BA 2022), Srishti G(BA 2022)

Syllabus

Definition and examples of Stochastic processes. General properties of Stochastic process like independent increment and stationary increment properties.

Introduction to Discrete time Markov chains: Definition, examples. Chapman-Kolmogorov equation. Absorbing state theory. State structure of finite state markov chains, theorems on transience and positive recurrence, ergodic and stationary properties.

Poisson processes and theorems related to waiting times under various conditions. Thinning and superposition properties of Poisson processes.

Continuous time Markov chains: Chapman-Kolmogorov. Rate transition matrix along with Kolmogorov backward/forward differential equations. ODE approach to CTMC and matrix exponentials. Poisson process as a CTMC. Birth-Death processes.

Wiener process and intro to Brownian motion.

Course Objectives

The fundamental objective of the course is to expose undergraduates to random processes and probability theory techniques used to analyse such processes. Since most phenomena in economics and finance are studied over time, the course is designed to enable the students to identify crucial properties of a stochastic process and compute relevant quantities.

References

• Sheldon M. Ross; “Introduction to Probability Models”, Academic Press, Ninth Edition, 2007.

Assignments

• Week 1
• Week 2
• Week 3
• Week 4
• Week 5
• Week 8
• Week 9
• Week 10
• Week 11
• Week 12
• Week 13

Main Tests

• Welcome test: A test for prerequisites in discrete probability theory and random variables.
• Internal I: Students were tested on Discrete-time Markov chains, independent increment and stationary increment properties of a stochastic process.
• Internal II: Axioms of probability theory and continuous distributions, Poisson process, CTMC and Chapman-Kolmogorov equations, differential equation viewpoint of CTMCs.
• Finals: All the syllabi of the internals and additionally Brownian motion.

Results

Three students scored the highest grades. Undergraduate students usually find this course hard, and my course was challenging because there was no proper reference material. However, I am pleased with the final paper. Lots of students surprised me with their understanding of the subject.

Many students who have scored below B+ may have no understanding of stochastic processes at all. If an employer or college wants to inquire about one of my students’ relative standing, please mail me.