Introduction to Stochastic Processes Course | IIT Bombay | Prof. Manjesh Hanawal
Course Details
| Exam Registration | 21 |
|---|---|
| Course Status | Ongoing |
| Course Type | Elective |
| Language | English |
| Duration | 12 weeks |
| Categories | Management Studies, Economics & Finance |
| Credit Points | 3 |
| Level | Postgraduate |
| Start Date | 19 Jan 2026 |
| End Date | 10 Apr 2026 |
| Enrollment Ends | 02 Feb 2026 |
| Exam Registration Ends | 20 Feb 2026 |
| Exam Date | 26 Apr 2026 IST |
| NCrF Level | 4.5 — 8.0 |
Master the Mathematics of Randomness: An Introduction to Stochastic Processes
In our daily lives, we constantly encounter uncertainty. How long will you wait for the next bus? What will be the traffic on your commute? Will your stock portfolio gain or lose value tomorrow? These questions don't have fixed answers because they involve random events beyond our direct control. The powerful mathematical framework used to model, analyze, and predict the behavior of such random systems over time is known as Stochastic Processes.
This detailed guide introduces a comprehensive 12-week postgraduate course on this very subject, offered by the prestigious Indian Institute of Technology (IIT) Bombay and instructed by Prof. Manjesh Kumar Hanawal. Whether you're in management, finance, economics, or engineering, this course provides the foundational tools to understand and leverage randomness.
Meet Your Instructor: Prof. Manjesh K. Hanawal
The course is led by an accomplished academic and researcher, ensuring you learn from an expert at the forefront of the field.
Prof. Manjesh K. Hanawal is an Assistant Professor in the Department of Industrial Engineering and Operations Research at IIT Bombay. He holds an M.S. in ECE from the Indian Institute of Science, Bangalore, and a Ph.D. from INRIA, Sophia Antipolis, and the University of Avignon, France. Following his doctorate, he completed postdoctoral research at Boston University.
His research expertise spans performance evaluation, machine learning, and network economics. A recognized scholar, Prof. Hanawal is a recipient of the prestigious Inspire Faculty Award from DST and the Early Career Research Award from SERB. His deep theoretical knowledge and applied research experience make him the ideal guide for this journey into stochastic modeling.
Who Is This Course For?
This course is meticulously designed for a broad audience:
- Postgraduate Students in Management, Economics, Finance, Operations Research, Industrial Engineering, Computer Science, and Electrical Engineering.
- Professionals & Analysts in fields like quantitative finance, risk management, data science, supply chain, and telecommunications who seek to strengthen their analytical modeling skills.
- All Disciplines Learners with the necessary mathematical curiosity and prerequisites.
Pre-requisite: A foundational understanding of Introductory Real Analysis and basic probability is recommended to fully grasp the course material.
Detailed 12-Week Course Curriculum
The course is structured to build your knowledge from fundamental probability concepts to advanced stochastic process theory. Here is a week-by-week breakdown:
| Week | Topics Covered |
|---|---|
| Week 1 | Introduction to Events, Probability, Conditional Probability, Bayes' Rule |
| Week 2 | Random Variables, Expectations, Variance, Various Types of Distributions |
| Week 3 | CDF and PDF of Random Variables, Conditional CDFs and PDFs |
| Week 4 | Jointly Distributed Random Variables, Covariance and Independence |
| Week 5 | Transformation of Random Variables and Their Distributions |
| Week 6 | Introduction to Random Processes, Stationarity and Ergodicity |
| Week 7 | Convergence of Sequences of RVs (Almost Surely, In Probability, In Distribution) |
| Week 8 | Strong and Weak Law of Large Numbers, Central Limit Theorem |
| Week 9 | Discrete Markov Chains, Stopping Time, Strong Markov Property, Classification of States |
| Week 10 | Counting Processes, Poisson Processes and Their Applications |
| Week 11 | Renewal Theory, Elementary and Renewal Reward Theorems |
| Week 12 | Introduction to Continuous-Time Markov Chains |
Key Learning Outcomes
By the end of this 12-week journey, you will be equipped to:
- Formulate and solve problems involving uncertainty using advanced probability theory.
- Understand and apply core concepts like Markov Chains to model state-dependent random systems.
- Utilize Poisson and Renewal Processes to model arrival and event patterns in queues, networks, and finance.
- Comprehend fundamental limit theorems like the Law of Large Numbers and the Central Limit Theorem.
- Analyze the long-term behavior and stability of stochastic systems.
Recommended Textbooks
To supplement the video lectures and assignments, the following classic texts are highly recommended:
- Introduction to Probability Models by Sheldon Ross
- Random Processes for Engineers by Bruce Hajek
Industry Relevance and Applications
Stochastic processes are not just theoretical constructs; they are vital tools across industries. This foundational course is recognized for its applicability in:
- Finance & Economics: Modeling stock prices, risk assessment, and algorithmic trading.
- Operations & Supply Chain Management: Optimizing inventory levels, queue management, and logistics.
- Data Science & Machine Learning: Underpinning algorithms for hidden Markov models, reinforcement learning, and time-series forecasting.
- Telecommunications: Network traffic modeling and performance analysis.
Mastering stochastic processes provides a significant analytical edge, allowing you to make data-informed decisions in an unpredictable world. Enroll in this IIT Bombay course to build a rigorous understanding of the fascinating mathematics that governs randomness.
Enroll Now →