Hi, I am Manisha, a Prime Minister’s Research Fellow (PMRF) in the Department of Mathematics at the Indian Institute of Technology Bhilai. I am pursuing my PhD under the supervision of  Dr. Kuldeep Kumar Kataria, Associate Professor, IIT Bhilai. My research lies broadly in the areas of probability theory and stochastic processes. A major part of my research is devoted to the study of time-changed counting processes, particularly those that permit the occurrence of multiple arrivals within an infinitesimal time interval. Such models extend the classical Poisson framework and are useful in describing systems where events may occur in clusters or batches rather than individually. My work involves studying their probabilistic structure and long-term behaviour, along with exploring their potential applications.

In addition, I work on elephant random walk models, a class of non-Markovian random walks characterized by long-range memory effects. My research mainly focuses on understanding how different memory mechanisms influence the evolution and asymptotic behaviour of these processes. In particular, I study variants involving delayed memory, partial memory loss, and other non-uniform memory structures, with the aim of understanding how memory impacts diffusion and scaling limits in stochastic systems. Overall, my research aims to contribute to the theoretical development of modern stochastic processes and memory-dependent random systems.