Markov chain
Markov Chain
A Markov Chain (pronounced: /ˈmɑːrkɒf tʃeɪn/) is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event.
Etymology
The term "Markov Chain" is named after the Russian mathematician Andrei Markov, who first described this mathematical concept in 1906.
Definition
In a Markov Chain, the state of an experiment changes with time. Each state is a result of the previous state, and the probability of transition from one state to another is defined by a probability distribution. The defining characteristic of a Markov Chain is that the probability of transitioning to any particular state depends solely on the current state and time elapsed, and not on the sequence of states that preceded it. This specific kind of "memorylessness" is called the Markov property.
Related Terms
- Stochastic process: A mathematical object usually defined as a collection of random variables.
- Probability distribution: A mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.
- Markov property: A property of a type of stochastic process, named after the Russian mathematician Andrei Markov.
- Andrei Markov: A Russian mathematician best known for his work on stochastic processes.
Applications
Markov Chains have many applications as statistical models of real-world processes. They are used in various fields such as physics, chemistry, economics, statistics, and computer science. For instance, in medicine, Markov Chains can be used to model the progression of diseases, where each state represents a different stage of the disease.
External links
- Medical encyclopedia article on Markov chain
- Wikipedia's article - Markov chain
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