Titlebook: Mathematical Statistics and Probability Theory; Volume A Theoretical M. L. Puri,P. Révész,W. Wertz Conference proceedings 1987 D. Reidel Pu

Ordnance

,Uniform Integrability in Anscombe’s Theorem for Martingales, random index T., provided that T./n converges in probability to a finite constant. To obtain moment convergence in Anscombe’s theorem one needs uniform integrability results for standardized random sums, and we investigate this question of uniform integrability in the case of martingale differences

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On a Functional Equation Occurring in the Limit Theorem for Maxima with Random Indices,distribution G is given by.where A and F are probability distributions. Here we investigate some properties that distributions F and A must satisfy, for given G, in order that the above equation holds.

CHOIR

Comparison of Shift Experiments on a Banach Space,cy is shown to be the supremum of the deficiencies between shift experiments defined by finite dimensional marginal distributions. Further, Boll’s “convolution divisibility” criterion for the ordering “being more informative” is extended to infinite dimensional spaces. More detailed results are give

痛打

,On the σ-Fields Which are Larger than a Sufficient One, than a sufficient one does not remain to be sufficient. In [4] there is a sufficient condition to avoid this pathological nature. According to [4] if the Boolean algebra . (.) is complete and .⊂. is a sufficient σ-field, then every σ-field .⊃. for which . (.) is a complete subalgebra of . (.) is su

宣誓书

On the Properties of Marginal Densities and Conditional Moments of Elliptically Contoured Measures, to the conditional moments of the form:., where r > m and j.,...,j. are nonnegative integers..It turns out that these densities and moments are defined by certain functions of one variable. We study such properties of these functions as different iability and monotonicity..Using formulae defining c

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