markoff process
Noun: A Markoff process (also commonly spelled 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 only on the current state of the process, and not on the sequence of events that preceded it (its history).
This term is used primarily in mathematics, statistics, physics, computer science, and related fields to describe systems with stochastic (random) behavior that possesses the Markov property. * The evolution of the system can be modeled as a Markoff process. * In queueing theory, the arrival of customers is often assumed to follow a Markoff process. * The researcher used a Markoff process to simulate the random motion of particles.
- Markov Chain: A specific type of Markoff process that has a discrete (countable) state space. It is a sequence of possible events where the probability of each event depends only on the state attained in the previous event.
- Example: The board game "Snakes and Ladders" is a classic example of a Markov chain; your next position depends only on your current square and the roll of the die, not on how you got there.
- Hidden Markov Model (HMM): A statistical model in which the system being modeled is assumed to be a Markoff process with unobserved (hidden) states.
- Example: Hidden Markov Models are extensively used in speech recognition and bioinformatics.
- Markov process: The more common modern spelling. "Markoff process" is an older transliteration from the name of the Russian mathematician Andrey Markov.
- Markov property (n): The defining "memoryless" characteristic of a Markoff process.
- Stochastic process (n): A broader family of random processes of which the Markoff process is a specific, important type.
- Memoryless process
- Markovian process
- State Space: The set of all possible states of the system.
- 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.
- 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