Mathematical modeling, analysis, and application of probabilistic systems in Mathematics

Abstract

The mathematical modeling, analysis, and application of Understanding and forecasting the behaviour of complex real-world phenomena requires the use of probabilistic systems, which play an essential role in both of these endeavours. This area of research involves the creation of mathematical models that can account for unpredictability and randomness, the examination of these models in order to obtain new insights into the behaviour of the system, and the implementation of probabilistic systems in a variety of real-world settings. Researchers and practitioners can depict real-world systems with probabilistic variables and interactions using mathematical modelling, which enables a greater understanding of the dynamics of those systems. approaches of analysis, such as probability theory, statistical approaches, and optimisation, contribute to the quantification of uncertainties, the evaluation of performance, and the direction of decision-making. The use of probabilistic systems can be found in a wide variety of contexts, including the fields of finance, meteorology, epidemiology, manufacturing, transportation, and even artificial intelligence, to name a few. This abstract presents a summary of the mathematical modelling, analysis, and application of probabilistic systems. It also underlines the significance of these systems in the context of tackling complicated issues that arise in the actual world.