Markovlánc

Markovlánc is a concept in probability theory and statistics, named after the Russian mathematician Andrey Markov. It refers to a sequence of random variables where the probability of each event depends only on the state attained in the previous event, and not on the sequence of events that preceded it. This property is known as the Markov property.

In a Markov chain, each state has a transition probability that determines the likelihood of moving to another state. The chain is said to be in a stationary state if the transition probabilities do not change over time. Markov chains are widely used in various fields, including physics, biology, economics, and computer science, to model systems that exhibit memoryless behavior.

One of the key applications of Markov chains is in the analysis of stochastic processes. By modeling a system as a Markov chain, researchers can derive important properties such as steady-state probabilities, mean recurrence times, and absorption probabilities. Markov chains also play a crucial role in the design and analysis of algorithms, particularly in the field of machine learning, where they are used in techniques such as Markov chain Monte Carlo (MCMC) methods.

The Markov property is a fundamental concept in the study of stochastic processes and has numerous practical implications. By simplifying complex systems into a sequence of dependent random variables, Markov chains provide a powerful tool for understanding and predicting the behavior of various phenomena in the natural and social sciences.