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Transfer theorems and right-continuous processes
Teoriâ slučajnyh processov, Tome 21 (2016) no. 2, pp. 91-95 Cet article a éte moissonné depuis la source Math-Net.Ru

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A counterexample to a transfer result in [5] (Theorem 2.4, Chap. 4) is given. A new result, which provides a reasonable substitute for the disproved one, is proved as well. This result yields, in particular, a transfer theorem for processes whose paths are right-continuous but not necessarily cadlag.
Keywords: Coupling, perfect probability measure, regular conditional distribution, transfer theorem. 
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Pietro Rigo; Hermann Thorisson. Transfer theorems and right-continuous processes. Teoriâ slučajnyh processov, Tome 21 (2016) no. 2, pp. 91-95. http://geodesic.mathdoc.fr/item/THSP_2016_21_2_a7/

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[2] P. Berti, L. Pratelli, P. Rigo, “A survey on Skorokhod representation theorem without separability”, Theory Stoch. Proc., 20(36):2 (2015), 1–12

[3] O. Kallenberg, Foundations of modern probability, Second Edition, Springer, New York, 2002

[4] D. Ramachandran, Perfect measures I and II, ISI-Lect. Notes Series 5 and 7, Macmillan, New Delhi, 1979

[5] H. Thorisson, Coupling, stationarity, and regeneration, Springer, New York, 2000