Definition

1. Adjective:
   • Relating to or generated by a Markov process: The term "Markovian" describes a property, system, or sequence of events that possesses the characteristics of a Markov process. This fundamentally means that the future state depends only on the present state and not on the sequence of events that preceded it.

Usage Examples

• Adjective:
  • The system's behavior is Markovian, meaning its next state is determined solely by its current state.
  • They modeled the random walk using a Markovian assumption.
  • Not all stochastic processes are Markovian; some have long-term memory.

Advanced Usage

• "Markovian property": Also known as the "memoryless" property. It is the defining characteristic of a Markov process.

  • The Markovian property simplifies the analysis of the queueing model significantly.

• "Non-Markovian": Used to describe a process or system that does not have the Markov property, where future states depend on past history.

  • The system exhibited non-Markovian dynamics due to feedback loops.

Variants and Related Words

• Markov process (n): A stochastic process that satisfies the Markov property.

  • A Markov chain is a common type of Markov process with discrete states.

• Markov chain (n): A specific type of Markov process with a discrete state space.

  • The weather prediction model was built as a Markov chain.

Synonyms

• Memoryless: (In the context of stochastic processes) Having the property that the future is independent of the past given the present.
• Stochastic: Involving chance or probability. (Note: This is a broader term; all Markovian processes are stochastic, but not all stochastic processes are Markovian.)

Related Phrases

• Markovian decision process (MDP): A mathematical framework for modeling decision making in situations where outcomes are partly random and partly under the control of a decision maker, based on the Markov property.
  • Reinforcement learning algorithms often use a Markovian decision process as their foundation.

Related Concepts

• State space: The set of all possible states of a Markov process.
• Transition probability: The probability of moving from one state to another in a Markov process.

Adjective

1. relating to or generated by a Markov process