The word "Markovian" is often spelled with a "k" instead of a "c", which can be confusing for non-native speakers. In IPA phonetic transcription, the word is pronounced /mɑːrˈkəʊviən/, with the stress on the second syllable. The "k" represents the hard "k" sound, while the "o" in the second syllable is pronounced like the "o" in "go". The "v" represents a voiced labiodental fricative, which is made by placing your lower lip against your upper teeth and allowing air to pass through.
Markovian refers to a mathematical or statistical concept associated with a type of stochastic process known as a Markov process or Markov chain. Such processes exhibit the Markov property, which states that the future state of the system depends solely on its present state, and not on its past history. In other words, the events or states in a Markovian process are memoryless and independent of previous states once the current state is known.
The term "Markovian" originates from the work of the Russian mathematician Andrey Markov, who laid the foundation for this theory in the early 20th century. Markovian processes are widely used in various fields of study, particularly in probability theory, statistics, physics, computer science, and engineering.
In a Markovian system, the future state can be predicted or estimated using transition probabilities, which describe the likelihood of transitioning from one state to another. These probabilities are typically represented in the form of a transition matrix or transition diagram. The simplicity and elegance of Markovian models make them valuable tools for modeling and analyzing many real-world phenomena, including weather patterns, financial markets, queueing systems, and language processing.
Overall, "Markovian" refers to a system or process that conforms to the Markov property, where the future state is determined solely by the present state, disregarding any past events or states.
The term "Markovian" is derived from the name of the Russian mathematician Andrey Markov. Andrey Markov (1856-1922) was known for his research in probability theory and its application to the study of sequences of random events. He introduced the concept of Markov chains, which are mathematical models used to describe sequences of events where the probability of each event only depends on the state of the previous event. The adjective "Markovian" is used to describe phenomena or systems that exhibit the properties or characteristics of Markov chains.