MR0314115 (47 #2667) Vasershtein, L. N.
Markov processes over denumerable products of spaces describing large system of automata.
Problems of Information Transmission 5 (1969), no. 3, 47–52; translated from Problemy Peredači Informacii 5 (1969), no. 3, 64--72 (Russian) 60J05 (94A35)
is cited in 29 publications:
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MR2996972 Prelim Ebner, Oliver; Convergence of refinement schemes on metric spaces. Proc. Amer. Math. Soc. 141 (2013), no. 2, 677–686.
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MR2854323 Reviewed Mileyko, Yuriy; Mukherjee, Sayan; Harer, John Probability measures on the space of persistence diagrams. Inverse Problems 27 (2011), no. 12, 124007, 22 pp. (Reviewer: Gutti J. Babu) 60B05 (60B99 62H11)
MR2779833 Reviewed Abourashchi, N.; Veretennikov, A. Yu. On stochastic averaging and mixing. Theory Stoch. Process. 16 (2010), no. 1, 111–129. (Reviewer: Athanasios Yannacopoulos) 60H30 (37A25)
MR2594441 Indexed Cohen-Steiner, David; Edelsbrunner, Herbert; Harer, John; Mileyko, Yuriy Lipschitz functions have
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MR2251231 Reviewed van Breugel, Franck; Worrell, James Approximating and computing behavioural distances in probabilistic transition systems. Theoret. Comput. Sci. 360 (2006), no. 1-3, 373–385. (Reviewer: Andrea Maggiolo-Schettini) 68Q85 (28A33 68Q60)
MR2237206 Reviewed Sturm, Karl-Theodor On the geometry of metric measure spaces. I. Acta Math. 196 (2006), no. 1, 65–131. (Reviewer: Juha Heinonen) 53C23
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MR2207064 Reviewed Bisin, Alberto; Horst, Ulrich; Özgür, Onur Rational expectations equilibria of economies with local interactions. J. Econom. Theory 127 (2006), no. 1, 74–116. (Reviewer: Susheng Wang) 91A10 (91A15 91B62)
MR2120054 Reviewed van Breugel, Franck; Worrell, James A behavioural pseudometric for probabilistic transition systems. Theoret. Comput. Sci. 331 (2005), no. 1, 115–142. 68Q60 (03B45 28A33 54E70 60J05 68Q55)
MR2108858 Reviewed Louis, Pierre-Yves Ergodicity of PCA: equivalence between spatial and temporal mixing conditions. Electron. Comm. Probab. 9 (2004), 119–131 (electronic). (Reviewer: Utkir Rozikov) 60G60 (37B15 37H99 60J10 60K35 68Q80 82C20 82C26)
MR2107899 Reviewed Eizenberg, A.; Kifer, Y. Large deviations for probabilistic cellular automata. II. J. Statist. Phys. 117 (2004), no. 5-6, 845–889. (Reviewer: Vadim A. Kaĭmanovich) 60F10 (37A50 37B15 68Q80 82C99)
MR2065028 Reviewed Toscani, Giuseppe Kinetic and hydrodynamic models of nearly elastic granular flows. Monatsh. Math. 142 (2004), no. 1-2, 179–192. 82C40 (76P05 76T25)
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MR0298716 (45 #7765) Reviewed
Dobrušin, R. L.
Definition of a system of random variables by means of conditional distributions. (Russian. English summary)
Teor. Verojatnost. i Primenen. 15 (1970), 469–497.
60B05
The author continues his earlier researches [Teor. Verojatnost. i Primenen. 13 (1968), 201–229; MR0231434 (37 #6989)] into the conditions for existence and uniqueness of a random field with a given system of conditional distributions. He now considers different conditions for the weak dependence of a random field. For the formulation of his results the author studies and makes use of an interesting metric (the Vaseršteĭn metric) in the space of all probability distributions on (X,B), where X is a metric space with metric ρ(x,y) and B is an algebra of Borel sets in X. Let P and Q be probability distributions on (X,B) and R(P,Q)=infEρ(ξ,η), where the infimum is taken over all ξ and η with values in X such that ξ has distribution P, and η has distribution Q. R(P,Q) is called the Vaseršteĭn distance.
{This article has appeared in English translation [Theor. Probability Appl. 15 (1970), 458–486].}
Reviewed by M. I. Jadrenko