EXISTENCE OF PROBABILITY-MEASURES WITH GIVEN MARGINALS
成果类型：
Article
署名作者：
GUTMANN, S; KEMPERMAN, JHB; REEDS, JA; SHEPP, LA
署名单位：
AT&T; Nokia Corporation; Nokia Bell Labs; Rutgers University System; Rutgers University New Brunswick
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176990236
发表日期：
1991
页码：
1781-1797
关键词：
摘要：
We show that if f is a probability density on R(n) wrt Lebesgue measure (or any absolutely continuous measure) and 0 less-than-or-equal-to f less-than-or-equal-to 1, then there is another density g with only the values 0 and 1 and with the same (n - 1)-dimensional marginals in any finite number of directions. This sharpens, unifies and extends the results of Lorentz and of Kellerer. Given a pair of independent random variables 0 less-than-or-equal-to X, Y less-than-or-equal-to 1, we further study functions 0 less-than-or-equal-to phi less-than-or-equal-to 1 such that Z = phi(X, Y) satisfies E(Z\X) = X and E(Z\Y) = Y. If there is a solution then there also is a nondecreasing solution phi(x, y). These results are applied to tomography and baseball.