Course: Modern Methods in Probability Theory [May 12th - 17th, 2025]

In this series of lectures we will introduce two important topics in modern probability theory viz. Markov chains and Martingale theory. Both of these notions are dependent on the notion of ‘conditional probabilities’ and ‘conditional expectations’ which in turn rests on the measure theoretic notion of a ‘Radon Nikodym Derivative’. Having introduced the notions of ‘Markov chains’ and ‘Martingales’, we introduce models of stochastic processes in continuous time, prime examples being Brownian motion and the Poisson process. We end the series with a discussion on stochastic differential equations and stochastic partial differential equations.

Instructor: Rajeev Bhaskaran, IISER TVM

Background required: No background in measure theory or advanced probability is required, though familiarity with these topics will be helpful. The course assumes basic knowledge of calculus, linear algebra, and elementary probability—such as integrals, matrices, and random variables. More advanced concepts, including conditional expectations and the Radon-Nikodym derivative, will be introduced as needed. MSc students, PhD scholars and young faculty members are eligible to apply. 

Deadline for application: May 05, 2025.  

The list of selected candidates will be available on the website by 07th May 2025. 

Selected candidates are listed below.