DA 244 Applied Probability and Stochastic Processes

Course Description

The course is broadly divided into 3 modules:

• Module 1 Review of Probability
• Module 2 Random Number Generation
• Module 3 Random Processes

Course Syllabus

Review of basic probability: Random variables and random vectors, Classical Inequalities and limit theorems

Random Number Generation; Generation of Random Variables: Inverse Transform method, Acceptance- rejection method, Variance Reduction methods: Control Variate, Conditioning, Importance Sampling; Uncertainty, Entropy.

Random Processes: Definition and classification of random processes, Autocorrelation and properties, Random process through LTI systems, Bernoulli processes, Markov Chains (MCs): Preliminaries, Discrete-time MC: Transition Probability Matrix, Classification of states, Chapman-Kolmogorov Equation, Limiting & stationary Distributions, Ergodic MC; Continuous time MC: Poisson Process, Weiner process, Birth and Death Processes; Application and Case Studies.

Course Logistics

• Schedule: Slot D, 9:00 am - 9:55 am Thursday, 10:00 am - 10:55 am Friday, 11:00 am - 11:55 am Monday
• Venue: 5103, Core 5.

Course Evaluation

• Attendance: 10%
• Quizzes: 30%
• Mid semester exam: 30%
• End semester exam: 30%

Some references (not an exhaustive list)

• Ross, S.M., 2022. Simulation. Academic Press.
• Ross, S.M., 1995. Stochastic processes. John Wiley & Sons.
• Bertsekas, D. and Tsitsiklis, J.N., 2008. Introduction to probability (Vol. 1). Athena Scientific.
• Prof. Dootika Vats notes on Statistical Computing
• Blitzstein, J.K., and Hwang J., 2019. Introduction to probability. Taylor & Francis Group, LLC.

Topics Covered during the weeks