Description: A Markov chain is a stochastic process that describes a series of events where the probability of moving from one state to another depends solely on the current state and not on previous states. This concept is based on the Markov property, which states that the future is independent of the past, given the present. Markov chains are commonly represented by a set of states and a transition matrix that defines the probabilities of moving from one state to another. This model is fundamental in various fields such as probability theory, statistics, and machine learning, as it allows for modeling dynamic systems and predicting future behaviors based on historical data. Markov chains can be discrete or continuous, depending on whether the states are finite or infinite. Their simplicity and versatility make them powerful tools for predictive analysis and simulation, facilitating the understanding of complex phenomena in fields such as economics, biology, and artificial intelligence.
History: The concept of Markov chains was introduced by Russian mathematician Andrey Markov in 1906. Markov studied stochastic processes and developed the theory that bears his name to describe systems where the future depends only on the present. Throughout the 20th century, Markov chains expanded into various disciplines, including queue theory, economics, and biology, becoming a fundamental tool in statistics and probability theory.
Uses: Markov chains are used in a wide variety of applications, including modeling queue systems, predicting time series, analyzing data in various fields, and simulating stochastic processes. They are also fundamental in machine learning, where they are applied in reinforcement learning algorithms, natural language processing, and more.
Examples: A practical example of Markov chains is the weather prediction model, where the current state of the weather is used to predict future weather. Another example is Google’s PageRank algorithm, which uses Markov chains to determine the relevance of web pages based on the links between them.
