# Markov Chain

## Definition of Markov Chain

A Markov chain is a mathematical model for sequences of random events, where the probability of any event depends only on the immediately preceding event.

## How is Markov Chain used?

Markov Chain is a type of machine learning algorithm that uses probability to model complex systems. It is based on the assumption that future states are determined by the previous state. In essence, it is a way to predict future states or events in sequence based on past events or states.

Markov Chains are used in many applications, from speech recognition and natural language processing to image segmentation and video recommendation. The key idea behind Markov Chains is that if we know the current state, then we can make predictions about the next state without considering any additional information.

Markov Chains have been applied in various fields such as finance, physics, artificial intelligence and operations research. In finance, they have been used for portfolio optimization, credit rating prediction and stock market price prediction. In physics, they are used to study thermodynamic systems and reaction kinetics. In AI and operations research they have been employed in robotics, decision trees and games like Go or Chess.

In terms of operation, Markov Chains rely on transition matrices which assign probabilities to each possible transition between two states in a system. These transition matrices are created by analyzing data about how frequently one state moves into another over time. By using this information to create a probability distribution for each state given the previous one, a Markov Chain can be defined from its initial state onward. Once this chain has been established it can be used to predict future states with a certain degree of accuracy given enough data points from different sources.