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  2. Stochastic matrix - Wikipedia

    en.wikipedia.org/wiki/Stochastic_matrix

    A substochastic matrix is a real square matrix whose row sums are all ; In the same vein, one may define a probability vector as a vector whose elements are nonnegative real numbers which sum to 1. Thus, each row of a right stochastic matrix (or column of a left stochastic matrix) is a probability vector.

  3. Markov chain - Wikipedia

    en.wikipedia.org/wiki/Markov_chain

    In probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event.

  4. 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.

  5. 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]

  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.

  7. Matrix analytic method - Wikipedia

    en.wikipedia.org/wiki/Matrix_analytic_method

    [1] [2] Such models are often described as M/G/1 type Markov chains because they can describe transitions in an M/G/1 queue. [ 3 ] [ 4 ] The method is a more complicated version of the matrix geometric method and is the classical solution method for M/G/1 chains.

  8. Doubly stochastic matrix - Wikipedia

    en.wikipedia.org/wiki/Doubly_stochastic_matrix

    There is a simple generalisation to matrices with more columns and rows such that the i th row sum is equal to r i (a positive integer), the column sums are equal to 1, and all cells are non-negative (the sum of the row sums being equal to the number of columns). Any matrix in this form can be expressed as a convex combination of matrices in ...

  9. Markov model - Wikipedia

    en.wikipedia.org/wiki/Markov_model

    The simplest Markov model is the Markov chain.It models the state of a system with a random variable that changes through time. In this context, the Markov property indicates that the distribution for this variable depends only on the distribution of a previous state.