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  2. Markov chain - Wikipedia

    en.wikipedia.org/wiki/Markov_chain

    If the Markov chain is time-homogeneous, then the transition matrix P is the same after each step, so the k-step transition probability can be computed as the k-th power of the transition matrix, P k. If the Markov chain is irreducible and aperiodic, then there is a unique stationary distribution π. [41]

  3. Markov model - Wikipedia

    en.wikipedia.org/wiki/Markov_model

    In this context, the Markov property indicates that the distribution for this variable depends only on the distribution of a previous state. An example use of a Markov chain is Markov chain Monte Carlo, which uses the Markov property to prove that a particular method for performing a random walk will sample from the joint distribution.

  4. Markovian arrival process - Wikipedia

    en.wikipedia.org/wiki/Markovian_arrival_process

    The Markov-modulated Poisson process or MMPP where m Poisson processes are switched between by an underlying continuous-time Markov chain. [8] If each of the m Poisson processes has rate λ i and the modulating continuous-time Markov has m × m transition rate matrix R , then the MAP representation is

  5. Markov Chains and Mixing Times - Wikipedia

    en.wikipedia.org/wiki/Markov_Chains_and_Mixing_Times

    The mixing time of a Markov chain is the number of steps needed for this convergence to happen, to a suitable degree of accuracy. A family of Markov chains is said to be rapidly mixing if the mixing time is a polynomial function of some size parameter of the Markov chain, and slowly mixing otherwise. This book is about finite Markov chains ...

  6. Examples of Markov chains - Wikipedia

    en.wikipedia.org/wiki/Examples_of_Markov_chains

    A game of snakes and ladders or any other game whose moves are determined entirely by dice is a Markov chain, indeed, an absorbing Markov chain. This is in contrast to card games such as blackjack, where the cards represent a 'memory' of the past moves. To see the difference, consider the probability for a certain event in the game.

  7. Markov reward model - Wikipedia

    en.wikipedia.org/wiki/Markov_reward_model

    In probability theory, a Markov reward model or Markov reward process is a stochastic process which extends either a Markov chain or continuous-time Markov chain by adding a reward rate to each state. An additional variable records the reward accumulated up to the current time. [1]

  8. Markov chains on a measurable state space - Wikipedia

    en.wikipedia.org/wiki/Markov_chains_on_a...

    In 1953 the term Markov chain was used for stochastic processes with discrete or continuous index set, living on a countable or finite state space, see Doob. [1] or Chung. [2] Since the late 20th century it became more popular to consider a Markov chain as a stochastic process with discrete index set, living on a measurable state space. [3] [4] [5]

  9. Discrete-time Markov chain - Wikipedia

    en.wikipedia.org/wiki/Discrete-time_Markov_chain

    A Markov chain with two states, A and E. In probability, a discrete-time Markov chain (DTMC) is a sequence of random variables, known as a stochastic process, in which the value of the next variable depends only on the value of the current variable, and not any variables in the past.