A stochastic process is a measurable phenomenon that develops randomly in time, and such processes can have widespread application and value. The ability to predict probable outcomes of random variables over time has a huge impact on sectors such as finance, healthcare and engineering.
Dr Abhishek Pal Majumder specialises in applied statistics and probability, with research topics including stochastic processes, time series models and econometric models.
Stochastic processes are essential tools for quantitative business forecasting based on historical data. They can be used in many ways to identify future trends in an uncertain environment, including: predicting future event patterns, such as the evolution of an epidemic; estimating future business performance; providing market traders with insight to make informed investments; and predicting housing prices.
Regime switching stochastic processes
Abhishek’s research focusses on regime switching stochastic processes, applying theory to address problems, for instance, in quantitative finance, actuarial science, economics, biology and ecology. Regime switching models demonstrate structural changes in a time series through different latent states. For example, this could mean the data-generating process is observed in both positive and negative economic growth, allowing us to see how changes in the underlying regime can impact the relevant characteristic of the observed process.
“My research goal is to analyse how different aspects of latent structures change the long-term behaviour of the overall stochastic process, by looking at causes and their effects of random events or phenomena. In statistics, my research is motivated by questions related to stochastic dynamical systems where the parameters that characterise overall stability of the systems, fluctuate over time driven by an underlying latent process.”
Addressing real-world problems in teaching
In his teaching, Abhishek provides students with the tools to solve problems from a variety of applications like molecular motion, population dynamics, weather, and finances.
“By using different applications in physical and biological sciences, we address questions like: how fast can an epidemic spread, what will be the stock price of a share in near future, and how can the forecasting of weather be modelled?”