Markov process
Definition
Noun: A Markov process is a mathematical model for a system that undergoes transitions from one state to another. It is characterized by the "memoryless" property, meaning the probability distribution of future states depends solely on the current state of the process, not on the sequence of events that preceded it.
Usage
The term is used in probability theory, statistics, and various applied fields like economics, queuing theory, and information science to model random systems that evolve over time. * The researcher used a Markov process to model the random movement of particles. * Predicting the next word in some language models can be treated as a Markov process.
Advanced Usage
- Markov property: The defining "memoryless" characteristic of a Markov process.
- The model's accuracy relies on the assumption of the Markov property.
- Markov chain: A specific, common type of Markov process that has a discrete (countable) state space. Often, the terms are used interchangeably, though "chain" specifies discreteness.
- The board game simulation was built using a Markov chain with each square as a state.
Variants and Related Words
- Markovian (adjective): Having the properties of a Markov process; memoryless.
- We assume the system's dynamics are Markovian.
- Semi-Markov process: A generalization where the time spent in a state can follow an arbitrary distribution before a Markovian transition occurs.
Synonyms
- Memoryless process
- Markov chain (when the state space is discrete)
Related Concepts (Not Phrasal Verbs/Idioms)
- State space: The set of all possible states the process can be in.
- Transition probability: The probability of moving from one state to another.
- Stationary distribution: A probability distribution that remains unchanged as the process evolves over time.
Noun
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a simple stochastic process in which the distribution of future states depends only on the present state and not on how it arrived in the present state
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