Markovn.

1938 Trans. Amer. Math. Soc. 44 102 Markoff processes are sometimes carelessly discussed in the literature as if they were the general case.

1939 Japanese Jrnl. Math. 16 47 (heading) Markoff process with an enumerable infinite number of possible states.

1950 W. Feller Introd. Probability Theory I. xv. 337 A Markov process is the probabilistic analogue of the processes of classical mechanics, where the future development is completely determined by the present state and is independent of the way in which the present state has developed.

1956 Nature 4 Feb. 207/1 The most simple case is when all the atoms of the assembly are supposed to have no volume and no interactions (such as in an ideal gas). In that case it can be treated as a Markov process.

1992 C. J. Wells Use Orthographic & Lexical Information (BNC) They model English text as a Markov process which allows transition probabilities to be assigned to various letter combinations and n-grams.

1938 Amer. Math. Monthly 45 410 Professor Allen considered probabilities which depend on the outcome or on the probability of previous events. Certain classical problems are of this type, but the Markoff chain was the first to be intensively studied.

1942 Trans. Amer. Math. Soc. 52 37 Then p_ij(t) can be considered a transition probability of a Markoff chain: A system is supposed which can assume various numbered states, and p_ij(t) is the probability that the system is in the jth state at the end of a time interval of length t, if it was in the ith state at the beginning of the interval.

1953 J. L. Doob Stochastic Processes v. 170 A Markov chain is defined as a Markov process..whose random variables can (with probability 1) only assume values in a certain finite or denumerably infinite set. The set is usually taken, for convenience, to be the integers 1,…, N (finite case) or the integers 1, 2,…(infinite case).

1953 J. L. Doob Stochastic Processes v. 186 The problem of card mixing is a good example of the application of Markov chains.

1960 J. G. Kemeny & J. L. Snell Finite Markov Chains ii. 25 A finite Markov chain is a finite Markov process such that the transition probabilities p_ij(n) do not depend on n.

1968 P. A. P. Moran Introd. Probability Theory iii. 140 Thus a Markov chain observed in the reverse direction of time will be a Markov process. However, it will not in general be a Markov chain because the observed transition probabilities will not be independent of t.

1973 Manch. Sch. Econ. & Social Stud. 41 401 (heading) A Markov chain model of the benefits of participating in government training schemes.

1991 Acta Metallurgica et Materialia 39 2547/1 The Monte Carlo algorithm..produces a series of snapshot atomic configurations appearing along the simulated Markov chain.

1944 Ann. Math. Statistics 15 237 The precise definition of this (Markoff) property is the following.

1950 W. Feller Introd. Probability Theory I. xv. 337 A definition of the Markov property.

1962 J. Riordan Stochastic Service Syst. iii. 28 The simplest infinite-server system is unique among its fellows in the possession of the Markov property that future changes are independent of the past.

1990 Q. Jrnl. Math. 41 109 The Markov property which plays such a large role in the theory of subfactors.