Discrete-time Markov Chains & Poisson Processes Course | IIT Guwahati
Course Details
| Exam Registration | 18 |
|---|---|
| Course Status | Ongoing |
| Course Type | Core |
| Language | English |
| Duration | 8 weeks |
| Categories | Mathematics |
| Credit Points | 2 |
| Level | Undergraduate/Postgraduate |
| Start Date | 19 Jan 2026 |
| End Date | 13 Mar 2026 |
| Enrollment Ends | 02 Feb 2026 |
| Exam Registration Ends | 16 Feb 2026 |
| Exam Date | 29 Mar 2026 IST |
| NCrF Level | 4.5 — 8.0 |
Mastering Discrete-time Markov Chains and Poisson Processes: An 8-Week Course Guide
Stochastic processes form the mathematical backbone for modeling randomness and uncertainty in countless real-world systems. From queue lengths at server farms to the spread of information in networks, understanding how systems evolve randomly over time is crucial. This detailed guide explores an intensive 8-week course on two foundational pillars of stochastic modeling: Discrete-time Markov Chains (DTMCs) and Poisson Processes, offered by esteemed faculty at IIT Guwahati.
Course Overview: Building a Foundation in Stochastic Modeling
This course is meticulously designed to take students from the basic definitions to advanced concepts like limiting probabilities and the properties of Poisson processes. The mathematical rigor is tailored for undergraduate students, making it accessible yet challenging. A solid grasp of calculus and basic probability is the essential prerequisite, ensuring all participants start from a common foundation of knowledge.
The course is not just an academic exercise; it has direct industry applications in Supply Chain management and Communications. Professionals in these fields, along with undergraduate and postgraduate students in Science and Engineering, will find the material immensely valuable for building models that predict system behavior under uncertainty.
Meet Your Instructors: Experts from IIT Guwahati
The course is led by two distinguished professors from the Department of Mathematics at IIT Guwahati, bringing a wealth of knowledge and teaching experience.
- Prof. Ayon Ganguly: An Assistant Professor specializing in Statistics, Prof. Ganguly has extensive experience teaching probability, statistics, stochastic processes, and Monte Carlo methods to both B.Tech. and M.Sc. students.
- Prof. Subhamay Saha: An Associate Professor and an expert in Probability and Stochastic Processes, Prof. Saha offers deep insights through his courses on probability, stochastic processes, and stochastic calculus.
Their combined expertise ensures the course balances theoretical depth with practical, illustrative examples and worked-out problems.
Detailed 8-Week Course Layout
The course is structured to progressively build your understanding week by week.
| Week | Topic | Key Focus Areas |
|---|---|---|
| 1 | Introduction to Discrete-time Markov Chains | Basic definitions, the Markov property, transition probabilities, and state spaces. |
| 2 | Communication | Understanding how states communicate with each other, leading to the concept of classes. |
| 3 | Hitting Times | Expected time to reach a particular state or set of states from a given starting point. |
| 4 | Classification of States | Transient vs. recurrent states, periodicity, and ergodicity. |
| 5 | Stationary Distribution | Finding long-run proportion of time spent in each state; solving equilibrium equations. |
| 6 | Limit Theorems | Convergence to stationary distributions and limiting probabilities. |
| 7 | Exponential Distribution & Counting Processes | The memoryless property, introduction to continuous-time processes. |
| 8 | Poisson Processes | Definitions, inter-arrival times, merging/splitting, and its relation to continuous-time Markov chains. |
Essential Reading and Resources
To complement the lectures, the course recommends two authoritative textbooks that are considered classics in the field:
- Introduction to Probability Models by Sheldon M. Ross (11th Edition). Renowned for its clarity and wealth of applied examples.
- Markov Chains by J. R. Norris. A concise yet rigorous treatment ideal for deepening theoretical understanding.
Who Should Take This Course?
This course is ideally suited for:
- Undergraduate students in Mathematics, Computing, Statistics, Engineering, and related fields.
- Postgraduate students looking to solidify their foundation in stochastic processes.
- Industry professionals in logistics, supply chain, telecommunications, data science, and finance who deal with stochastic modeling and queueing theory.
By the end of this 8-week journey, you will have a firm grasp of two of the most important stochastic processes. You'll be equipped to model systems where future states depend only on the present (Markov Chains) and model random events occurring continuously and independently over time (Poisson Processes). This knowledge is a powerful tool for analysis, prediction, and decision-making in an unpredictable world.
Enroll Now →