Splitting of liftings in products of probability spaces II

[摘要] 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. Musial, 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. Musial, 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 tau-additive measures, transfer of strong liftings, and stochastic processes. (C) 2007 Elsevier Inc. All rights reserved.

[发布日期] 2007-11-01

[关键词] product liftings and densities;regular conditional probability;strong liftings;product measures;tau-additive measures