Data Science Course: What is Markov chains? | Intellipaat

A Markov chain is a mathematical model that describes a sequence of events where the probability of each event depends only on the state of the system at the previous step, and not on the history of previous states. In other words, a Markov chain is a stochastic process that satisfies the Markov property.

A Markov chain can be represented by a directed graph, where each node represents a state of the system and the edges between the nodes represent the probabilities of transitioning from one state to another. The probabilities of transitioning from one state to another are given by the transition probabilities or transition matrix, which is a square matrix that specifies the probability of going from state i to state j.

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Markov chains are used in a wide range of applications, including physics, chemistry, biology, economics, and finance, among others. They have many interesting properties, including the existence of steady-state probabilities, which describe the long-term behavior of the system, and the convergence to a steady state, which is a stable state that the system eventually reaches and remains in thereafter.

Markov chains are also used in various algorithms, such as the PageRank algorithm used by Google to rank web pages, and the Hidden Markov Model used in speech recognition and natural language processing.