Applied Stochastic Processes Course | IIT Kharagpur | Prof. Swanand Khare & Prof. Amitalok Budkuley
Course Details
| Exam Registration | 52 |
|---|---|
| Course Status | Ongoing |
| Course Type | Elective |
| Language | English |
| Duration | 12 weeks |
| Categories | Mathematics |
| Credit Points | 3 |
| Level | Undergraduate |
| Start Date | 19 Jan 2026 |
| End Date | 10 Apr 2026 |
| Enrollment Ends | 02 Feb 2026 |
| Exam Registration Ends | 20 Feb 2026 |
| Exam Date | 19 Apr 2026 IST |
| NCrF Level | 4.5 — 8.0 |
Unlock the Power of Randomness: A Deep Dive into Applied Stochastic Processes
In a world increasingly driven by data and complex systems, understanding randomness is no longer a niche skill—it's a fundamental necessity. From optimizing network traffic and managing financial risk to modeling biological phenomena and AI algorithms, stochastic processes provide the essential mathematical framework. This is where the comprehensive 12-week course on Applied Stochastic Processes, offered by renowned faculty from the Indian Institute of Technology Kharagpur, becomes an invaluable resource for students and professionals alike.
Course Overview: Bridging Theory and Real-World Application
This undergraduate-level course is meticulously designed to introduce the core concepts of stochastic processes, focusing on systems that evolve randomly over time. It strikes a perfect balance between rigorous mathematical theory and practical, hands-on applications. Over 12 weeks, participants will journey from foundational probability reviews to advanced topics like Brownian motion and the Black-Scholes model, gaining tools directly applicable in fields like Electrical Engineering, Computer Science, Applied Mathematics, and Finance.
Learn from Distinguished IIT Kharagpur Faculty
The course is led by two esteemed professors, bringing together expertise from pure mathematics and cutting-edge engineering applications.
Prof. Swanand R. Khare is an Associate Professor in the Department of Mathematics and the Centre of Excellence in AI at IIT Kharagpur. With an M.Sc. and Ph.D. from IIT Bombay and post-doctoral experience at the University of Alberta, Canada, his research spans inverse eigenvalue problems, computational linear algebra, and applied statistics. A recipient of the Excellent Young Teacher Award (2018), Prof. Khare ensures the course's mathematical depth and clarity.
Prof. Amitalok J. Budkuley is an Assistant Professor in the Department of Electronics and Electrical Communication Engineering at IIT Kharagpur. Holding a Ph.D. from IIT Bombay and with research experience at The Chinese University of Hong Kong and Cisco Systems, his interests include wireless communications, information theory, and stochastic signal processing. Prof. Budkuley grounds the course in contemporary engineering challenges, particularly in communication networks and distributed systems.
Detailed 12-Week Course Curriculum
The course is structured to build knowledge progressively, with each week dedicated to a key topic, culminating in powerful applications.
| Week | Topics Covered |
|---|---|
| 1-2 | Preliminaries: Review of probability, key distributions (Bernoulli, Poisson, Exponential, Gaussian), conditional expectation, Central Limit Theorem, and software simulation. |
| 3-4 | Discrete-Time Markov Chains (DTMC): Definitions, Chapman-Kolmogorov equations, state classification, limiting probabilities, branching processes, and applications. |
| 5-6 | Counting Processes: Bernoulli and Poisson processes, their properties (merging, splitting), interarrival times, and applications to queueing. |
| 7-8 | Continuous-Time Markov Chains (CTMC): Birth-Death processes, Kolmogorov's equations, and limiting probabilities. |
| 9 | Renewal Theory: Definitions, limit theorems, renewal-reward theorem, and reliability applications. |
| 10 | Queueing Theory: Kendall notation, analysis of M/M/1 and other queue models. |
| 11 | Martingales & Brownian Motion: Definitions, Gambler's Ruin, Brownian motion with drift, Geometric Brownian Motion, Gaussian and stationary processes. |
| 12 | Financial Applications: Option pricing, Risk-neutral valuation, Arbitrage Theorem, and the Black-Scholes formula. |
Who Should Enroll?
This course is ideally suited for:
- Senior undergraduate and postgraduate students in Mathematics, Electronics & Communication (ECE), Electrical Engineering (EE), and Computer Science (CSE).
- Professionals and researchers in data science, telecommunications, finance, and operations research looking to solidify their foundational knowledge.
- Anyone with a prerequisite of an introductory course in Probability and Statistics seeking to understand the behavior of random systems.
Key Learning Outcomes and Applications
By the end of this course, you will be able to:
- Model and analyze systems using Discrete and Continuous-Time Markov Chains.
- Understand and work with fundamental random processes like the Poisson process, crucial for modeling arrival times in networks and service systems.
- Apply renewal theory to solve problems in reliability and maintenance.
- Analyze simple queueing models to predict system performance and bottlenecks.
- Comprehend the basics of Brownian motion and its pivotal role in financial mathematics for option pricing.
- Use stochastic processes to tackle real-world problems in communication networks, event-driven simulation, and financial engineering.
Recommended Textbooks
To complement the lectures, the instructors recommend the following authoritative texts:
- Ross, Sheldon M. Introduction to Probability Models. Elsevier. (A classic and highly accessible text).
- Gallager, Robert G. Stochastic Processes: Theory for Applications. Cambridge University Press.
- Ross, Sheldon M. Stochastic Processes. John Wiley & Sons.
- Gangopadhyay S. and Chandra T.K. Introduction to Stochastic Processes. Narosa Publishing House.
Embark on this 12-week journey to master the language of randomness. The Applied Stochastic Processes course from IIT Kharagpur is more than just a class; it's an investment in a skill set that will empower you to model, analyze, and innovate in an uncertain world. Enroll today and transform your understanding of dynamic random systems.
Enroll Now →