Markov chain ||Mathematics||

A Markov chain is a mathematical model that represents a system whose state transitions depend only on its current state and not on the sequence of events that preceded it. In other words, it is a stochastic process that undergoes transitions from one state to another in a probabilistic manner. The key components of a Markov chain are: States: A finite or countably infinite set of distinct states, which represent the possible conditions or situations of the system. The states can be discrete or continuous, depending on the nature of the system. Transition Probability Matrix: This matrix, often denoted by P, specifies the probabilities of transitioning from one state to another in a single step. If there are n states, the matrix is an n×n matrix, and each entry j. The sum of the probabilities in each row is always 1.Markov chains find applications in various fields such as physics, economics, biology, computer science, and more. They are used to model systems with random and sequential transitions, making them a powerful tool for analyzing and understanding dynamic processes.