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  2. Balance equation - Wikipedia

    en.wikipedia.org/wiki/Balance_equation

    For a continuous time Markov chain (CTMC) with transition rate matrix, if can be found such that for every pair of states and = holds, then by summing over , the global balance equations are satisfied and is the stationary distribution of the process. [5]

  3. Markov chain - Wikipedia

    en.wikipedia.org/wiki/Markov_chain

    A Markov chain is a type of Markov process that has either a discrete state space or a discrete index set (often representing time), but the precise definition of a Markov chain varies. [6]

  4. Detailed balance - Wikipedia

    en.wikipedia.org/wiki/Detailed_balance

    A Markov process is called a reversible Markov process or reversible Markov chain if there exists a positive stationary distribution π that satisfies the detailed balance equations [13] =, where P ij is the Markov transition probability from state i to state j, i.e. P ij = P(X t = j | X t − 1 = i), and π i and π j are the equilibrium probabilities of being in states i and j, respectively ...

  5. Discrete-time Markov chain - Wikipedia

    en.wikipedia.org/wiki/Discrete-time_Markov_chain

    Reversible Markov chains are common in Markov chain Monte Carlo (MCMC) approaches because the detailed balance equation for a desired distribution π necessarily implies that the Markov chain has been constructed so that π is a steady-state distribution.

  6. Continuous-time Markov chain - Wikipedia

    en.wikipedia.org/wiki/Continuous-time_Markov_chain

    A continuous-time Markov chain (CTMC) is a continuous stochastic process in which, for each state, the process will change state according to an exponential random variable and then move to a different state as specified by the probabilities of a stochastic matrix. An equivalent formulation describes the process as changing state according to ...

  7. Time reversibility - Wikipedia

    en.wikipedia.org/wiki/Time_reversibility

    Markov processes can only be reversible if their stationary distributions have the property of detailed balance: (=, + =) = (=, + =). Kolmogorov's criterion defines the condition for a Markov chain or continuous-time Markov chain to be time-reversible.

  8. Queueing theory - Wikipedia

    en.wikipedia.org/wiki/Queueing_theory

    The steady state equations for the birth-and-death process, known as the balance equations, are as follows. Here ... (the M denotes a Markov process).

  9. Markov property - Wikipedia

    en.wikipedia.org/wiki/Markov_property

    The term Markov assumption is used to describe a model where the Markov property is assumed to hold, such as a hidden Markov model. A Markov random field extends this property to two or more dimensions or to random variables defined for an interconnected network of items. [1] An example of a model for such a field is the Ising model.