Authors: Jag Pratap Singh Yadav
Abstract: Systems in reality are characterized by uncertainties. There are uncertainties associated with nature, economics, communications, healthcare delivery, production systems, and social systems, among others, which cannot be modeled using deterministic equations. Stochastic processes facilitate the formulation of mathematical models of systems whose behavior is affected by some random elements. They help in assessing risks, optimizing resource allocations, forecasting future behaviors, and enhancing system robustness. The paper centers on stochastic processes as techniques for dealing with uncertainty in systems. First, the concept of stochastic processes will be defined. Major types of stochastic processes, including Markov chains, Poisson processes, Brownian motion, random walks, and queueing models, will be discussed. Then, applications of stochastic models in various areas, such as financial modeling, engineering, health care, climate studies, operations management, telecommunications, and machine learning, will be explored. Additionally, this paper will examine advantages and disadvantages associated with stochastic modeling. In particular, problems associated with assumptions used in building stochastic models and computational complexities of such models will be analyzed. It will be concluded that stochastic processes represent powerful tools for studying and managing uncertain systems because they enable turning randomness from an issue into a quantifiable phenomenon.
DOI: https://doi.org/10.5281/zenodo.20021901
