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- W2046210481 abstract "A word function is a function from the set of all words over a finite alphabet into the set of real numbers. In particular, when the blocks of a partition over the state set of a Markov chain are taken as the letters of the finite alphabet, and the function represents the probabilities that the chain will visit sequences of such blocks consecutively, then the function is a function of a Markov chain. It is known that (the rank of a function is defined in the text), a word function is of “finite rank” if and only if it is a function of a pseudo Markov chain (“pseudo” means here that the initial vector and the matrix representing the chain may have positive, negative, or zero values and are not necessarily stochastic). The aim of this note is to show that any function of a pseudo Markov chain can be represented as the difference of two functions of true Markov chains multiplied by a factor which grows exponentially with the length of the arguments (considered as words over a finite alphabet)." @default.
- W2046210481 created "2016-06-24" @default.
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- W2046210481 date "1975-02-01" @default.
- W2046210481 modified "2023-09-30" @default.
- W2046210481 title "Word functions of pseudo-Markov chains" @default.
- W2046210481 cites W177913229 @default.
- W2046210481 doi "https://doi.org/10.1016/0024-3795(75)90089-0" @default.
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