DA 244 Applied Probability and Stochastic Processes

Course Description

The course is broadly divided into 2 modules:

• Module 1 Random Number Generation
• Module 2 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 E, 8:00 am - 8:55 am Tuesday, 9:00 am - 9:55 am Wednesday, 10:00 am - 10:55 am Thursday
• Venue: 5205, Core 5.

Course Evaluation

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

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.
• Blitzstein, J.K., and Hwang J., 2019. Introduction to probability. Taylor & Francis Group, LLC.

Tentative Lecture Plan