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  2. Examples of Markov chains - Wikipedia

    en.wikipedia.org/wiki/Examples_of_Markov_chains

    A finite-state machine can be used as a representation of a Markov chain. Assuming a sequence of independent and identically distributed input signals (for example, symbols from a binary alphabet chosen by coin tosses), if the machine is in state y at time n , then the probability that it moves to state x at time n + 1 depends only on the ...

  3. Markov chain - Wikipedia

    en.wikipedia.org/wiki/Markov_chain

    Markov chain models have been used in advanced baseball analysis since 1960, although their use is still rare. Each half-inning of a baseball game fits the Markov chain state when the number of runners and outs are considered. During any at-bat, there are 24 possible combinations of number of outs and position of the runners.

  4. 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 ...

  5. Absorbing Markov chain - Wikipedia

    en.wikipedia.org/wiki/Absorbing_Markov_chain

    A basic property about an absorbing Markov chain is the expected number of visits to a transient state j starting from a transient state i (before being absorbed). This can be established to be given by the (i, j) entry of so-called fundamental matrix N, obtained by summing Q k for all k (from 0 to ∞).

  6. Discrete phase-type distribution - Wikipedia

    en.wikipedia.org/wiki/Discrete_phase-type...

    A terminating Markov chain is a Markov chain where all states are transient, except one which is absorbing. Reordering the states, the transition probability matrix of a terminating Markov chain with m {\displaystyle m} transient states is

  7. Stochastic matrix - Wikipedia

    en.wikipedia.org/wiki/Stochastic_matrix

    Intuitively, a stochastic matrix represents a Markov chain; the application of the stochastic matrix to a probability distribution redistributes the probability mass of the original distribution while preserving its total mass. If this process is applied repeatedly, the distribution converges to a stationary distribution for the Markov chain.

  8. Uniformization (probability theory) - Wikipedia

    en.wikipedia.org/wiki/Uniformization...

    In probability theory, uniformization method, (also known as Jensen's method [1] or the randomization method [2]) is a method to compute transient solutions of finite state continuous-time Markov chains, by approximating the process by a discrete-time Markov chain. [2]

  9. 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.