Markov chain

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(Markoff), Andrei, Russian mathematician, 1865-1922.
Markov chain - number of steps or events in sequence.
Markov chaining - a theory used in psychiatry.
Markov process - a process such that the conditional probability distribution for the state at any future instant, given the present state, is unaffected by any additional knowledge of the past history of the system.

Markov chain, Markov model

a mathematical model that makes it possible to study complex systems by establishing a state of the system and then effecting a transition to a new state, such a transition being dependent only on the values of the current state, and not dependent on the previous history of the system up to that point.
References in periodicals archive ?
1] [less than or equal to] 1, where a value of 0 indicates that there is imperfect mobility or total persistence and this occurs when the elements of the leading diagonal of the transition probability matrix are equal to one.
The probabilities in each row of the transition probability matrix are mutually exclusive and collectively exhaustive, and thus the sum is one.
Note that if sensitivities had monotonically decreased from left to right across the transition probability matrix (as they may do in age-classified populations), one would, expect juveniles and prereproductives to have higher sensitivities than small reproductives.
4) The transition probability matrix A of hidden states, describes the transition probability between hidden states in HMM, where [a.
Next, we study the dynamics of the distribution and intradistributional mobility of regions by estimating a transition probability matrix.
in transition probability matrix of the tagger and assign this trigram to the window, disambiguating the output.
where P is the one-step transition probability matrix,
Such a problem arises in G/M/1 type Markov chains [26] having a transition probability matrix in block lower Hessenberg form, which is "almost" block Toeplitz.
The one-step transition probability matrix P of the MRW can be obtained directly from the affinity matrix W as follows:
where A is the transition probability matrix (now three dimensional), and x(t, t - 1) is a two-dimensional matrix describing the joint state distributions at times t and t - 1, and having the form shown in Fig.

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