This research explores the theoretical foundations of Markov chains and their potential application in modeling stochastic processes, with a particular focus on weather forecasting. The study establishes a comprehensive mathematical framework, examining the fundamental concepts of transition probabilities, state definitions, and the properties of transition matrices. Additionally, the research investigates the characteristics of ergodic, regular, and absorbing chains, alongside the role of stationary distributions. By conceptualizing a weather model based on three primary states sunny, cloudy, and rainy this work demonstrates how Markov processes can be utilized to generate short-term probabilistic forecasts. The study highlights that the Markov property provides an efficient and simplified approach to predicting future transitions based on current environmental states. The findings suggest that this methodology offers a robust alternative for atmospheric modeling, providing meaningful insights into weather patterns without requiring overly complex historical datasets.
