×

zbMATH — the first resource for mathematics

Probabilistic metric spaces induced by Markov chains. (English) Zbl 0314.60047

MSC:
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60B05 Probability measures on topological spaces
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Chung, K. L.: Markov chains with stationary transition probabilities. 2nd ed., Berlin-Heidelberg-New York: Springer 1967 · Zbl 0146.38401
[2] Karlin, S.: A first course in stochastic processes. New York: Academic Press 1969
[3] Menger, K.: Statistical metrics. Proc. Nat. Acad. Sci. USA, 28, 535-537 (1942) · Zbl 0063.03886 · doi:10.1073/pnas.28.12.535
[4] Schweizer, B.: Probabilistic metric spaces ? the first 25 years. The New York Statistician 19, 3-6 (1967)
[5] Schweizer, B.: Multiplications on the space of probability distribution functions. Aequationes Math. 12, 121-144 (1975) · Zbl 0308.39009 · doi:10.1007/BF01836543
[6] Schweizer, B., Sklar, A.: Probabilistic metric spaces determined by measure-preserving transformations. Z. Wahrscheinlichkeitstheorie verw. Gebiete 26, 235-240 (1973) · Zbl 0259.60004 · doi:10.1007/BF00532725
[7] ?erstnev, A. N.: The notion of a random normed space. Doklady Academia Nauk, USSR, 149, 280-283 (1963) [Translated in Soviet Math. Dokl. 4, 388-391]
[8] Sherwood, H.: Complete Probabilistic Metric Spaces. Z. Wahrscheinlichkeitstheorie verw. Gebiete 20, 117-128 (1971) · Zbl 0215.53103 · doi:10.1007/BF00536289
[9] Stevens, R. R.: Metrically generated probabilistic metric spaces. Fund. Math. 61, 259-269 (1968) · Zbl 0175.46504
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.