Title of the talk: "Fractional Poisson Models and Applications"

Date , Time & Venue: 6 August 2025, 10:00 AM, Seminar Hall, Dept. of Mathematics

Abstract: In this talk, we explore the Poisson process and its fractional counterpart, known as the fractional Poisson process (FPP), through the lens of fractional calculus. The FPP extends the memoryless nature of the Poisson process by introducing memory and long-range dependence, making it more suitable for modeling real-world phenomena with non-Markovian behavior. We highlight key properties of the FPP, and compare it with its time-fractional, space-fractional, and tempered variants. In particular, we emphasize the role of the tempered fractional Poisson process, which balances the heavy-tailed behavior of the standard FPP with exponential tempering, leading to more realistic modeling in certain applications. We discuss the use of the tempered FPP in modeling shock driven systems.

About the Speaker: Dr. Ritik Soni currently an Institute Postdoctoral Fellow in the Department of Mathematics and Statistics at  I.I.T.  Kanpur, where his research focuses on Markov Chain Monte Carlo (MCMC) methods. In parallel, he is also investigating the practical relevance of fractional stochastic models in various applied contexts. Prior to this, he  has a postdoctoral position at the Chennai Mathematical Institute. He obtained Ph.D. from the Central University of Punjab, Bathinda, where his doctoral research centered on fractional stochastic processes and their connections to non-local operators.