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  2. Markov chain - Wikipedia

    en.wikipedia.org/wiki/Markov_chain

    A discrete-time Markov chain is a sequence of random variables X 1, X 2, X 3, ... with the Markov property, namely that the probability of moving to the next state depends only on the present state and not on the previous states:

  3. 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 ...

  4. Markov model - Wikipedia

    en.wikipedia.org/wiki/Markov_model

    A Markov decision process is a Markov chain in which state transitions depend on the current state and an action vector that is applied to the system. Typically, a Markov decision process is used to compute a policy of actions that will maximize some utility with respect to expected rewards.

  5. 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 ...

  6. 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]

  7. Markov Chains and Mixing Times - Wikipedia

    en.wikipedia.org/wiki/Markov_Chains_and_Mixing_Times

    A Markov chain is a stochastic process defined by a set of states and, for each state, a probability distribution on the states. Starting from an initial state, it follows a sequence of states where each state in the sequence is chosen randomly from the distribution associated with the previous state.

  8. 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.

  9. Kolmogorov's criterion - Wikipedia

    en.wikipedia.org/wiki/Kolmogorov's_criterion

    Consider this figure depicting a section of a Markov chain with states i, j, k and l and the corresponding transition probabilities. Here Kolmogorov's criterion implies that the product of probabilities when traversing through any closed loop must be equal, so the product around the loop i to j to l to k returning to i must be equal to the loop the other way round,