THE MARKOV THEOREM AND THE LAW OF LARGE NUMBERS: FUNDAMENTAL PRINCIPLES AND DERIVED RESULTS

This article explores the fundamental principles and applications of the Law of Large Numbers (LLN) and the Markov Theorem. The LLN establishes the convergence of sample averages to expected values, while the Markov Theorem ensures the convergence of Markov Chains to stationary distributions. We discuss the theoretical underpinnings, practical applications in various fields, and future research directions, highlighting the importance of these concepts in understanding stochastic processes and making predictions.