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Splitting of liftings in products of probability spaces II |
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| Authors: | ND Macheras W Strauss |
| Institution: | a Department of Statistics and Insurance Science, University of Piraeus, 80 Karaoli and Dimitriou street, 185 34 Piraeus, Greece b Institute of Mathematics, Wroc?aw University, Pl. Grunwaldzki 2/4, 50-384 Wroc?aw, Poland c Universität Stuttgart, Fachbereich Mathematik, Institut für Stochastik und Anwendungen, Postfach 80 11 40, D-70511 Stuttgart, Germany |
| Abstract: | For a probability measure R on a product of two probability spaces that is absolutely continuous with respect to the product measure we prove the existence of liftings subordinated to a regular conditional probability and the existence of a lifting for R with lifted sections which satisfies in addition a rectangle formula. These results improve essentially some of the results from the former work of the authors W. Strauss, N.D. Macheras, K. Musia?, Splitting of liftings in products of probability spaces, Ann. Probab. 32 (2004) 2389-2408], by weakening considerably the assumptions and by presenting more direct and shorter proofs. In comparison with W. Strauss, N.D. Macheras, K. Musia?, Splitting of liftings in products of probability spaces, Ann. Probab. 32 (2004) 2389-2408] it is crucial for applications intended that we can now prescribe one of the factor liftings completely freely. We demonstrate the latter by applications to τ-additive measures, transfer of strong liftings, and stochastic processes. |
| Keywords: | Product liftings and densities Regular conditional probability Strong liftings Product measures τ-Additive measures |
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