Abstract
The purpose of this paper is to introduce some algebraic structure, as in Heller [12], in the class of Markovian stochastic processes in discrete time and countable state space. By this method the algebraic structure theory of stochastic modules is developed, and consequently some results are obtained about the reduced modules through the dimension of various subspaces of these modules when viewed as vector spaces over the real line. These results turn out to be conceptually simpler and elegant in form. Finally, the stochastic module theory developed is employed in the study of the decomposition of the reduced module of a stationary Markov chain, and the relationship between probability measures and linear functionals is studied.
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© 1977 ACADEMIA, Publishing House of the Czechoslovak Academy of Sciences, Prague
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Ahmad, R. (1977). An Algebraic Treatment of Markov Processes. In: Kožešnik, J. (eds) Transactions of the Seventh Prague Conference on Information Theory, Statistical Decision Functions, Random Processes and of the 1974 European Meeting of Statisticians. Transactions of the Seventh Prague Conference on Information Theory, Statistical Decision Functions, Random Processes and of the 1974 European Meeting of Statisticians, vol 7A. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9910-3_1
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DOI: https://doi.org/10.1007/978-94-010-9910-3_1
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