ar X iv : m at h / 06 06 60 4 v 1 [ m at h . PR ] 2 3 Ju n 20 06 0 - 1 LAWS FOR REGULAR CONDITIONAL DISTRIBUTIONS
نویسنده
چکیده
Abstract. Let (Ω,B, P ) be a probability space, A ⊂ B a sub-σ-field, and μ a regular conditional distribution for P given A. Necessary and sufficient conditions for μ(ω)(A) to be 0-1, for all A ∈ A and ω ∈ A0, where A0 ∈ A and P (A0) = 1, are given. Such conditions apply, in particular, when A is a tail sub-σ-field. Let H(ω) denote the A-atom including the point ω ∈ Ω. Necessary and sufficient conditions for μ(ω)(H(ω)) to be 0-1, for all ω ∈ A0, are also given. If (Ω,B) is a standard space, the latter 0-1 law is true for various classically interesting sub-σ-fields A, including tail, symmetric, invariant, as well as some sub-σ-fields connected with continuous time processes.
منابع مشابه
ar X iv : m at h / 06 06 33 9 v 1 [ m at h . SP ] 1 4 Ju n 20 06 Eigenfunction expansions associated with 1 d periodic differential operators of order 2 n
We prove an explicit formula for the spectral expansions in L(R) generated by selfadjoint differential operators (−1) d dx2n + n−1
متن کاملar X iv : m at h / 06 06 67 1 v 1 [ m at h . A C ] 2 7 Ju n 20 06 PRÜFER ⋆ – MULTIPLICATION DOMAINS AND ⋆ – COHERENCE
متن کامل
ar X iv : m at h / 04 06 08 3 v 3 [ m at h . PR ] 1 7 Ju n 20 05 Large deviations for empirical entropies of g - measures
The entropy of an ergodic finite-alphabet process can be computed from a single typical sample path x1 using the entropy of the k-block empirical probability and letting k grow with n roughly like logn. We further assume that the distribution of the process is a g-measure. We prove large deviation principles for conditional, non-conditional and relative k(n)-block empirical entropies.
متن کاملar X iv : m at h / 05 06 26 9 v 1 [ m at h . PR ] 1 4 Ju n 20 05 Percolation , boundary , noise : an experiment
The scaling limit of the critical percolation, is it a black noise? The answer depends on stability to perturbations concentrated along a line. This text, containing no proofs, reports experimental results that suggest the affirmative answer.
متن کامل