SUPPORTS OF CERTAIN INFINITELY DIVISIBLE PROBABILITY-MEASURES ON LOCALLY CONVEX-SPACES
成果类型：
Article
署名作者：
RAJPUT, BS
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176989272
发表日期：
1993
页码：
886-897
关键词：
摘要：
Let B be a separable Banach space and let mu be a centered Poisson probability measure on B with Levy measure M. Assume that M admits a polar decomposition in terms of a finite measure sigma on the unit sphere of B and a Levy measure rho on (0, infinity). The main result of this paper provides a complete description of the structure of l(mu), the support of mu. Specifically, it is shown that: (i) if integral(0, 1]srho(ds) = infinity, then l(mu) is a linear space and is equal to the closure of the semigroup generated by l(M) (the support of M) and the negative of the barycenter of sigma; and (ii) if integral(0, 1]srho(ds) < infinity and zero is in the support of rho, then l(mu) is a convex cone and is equal to the closure of the semigroup generated by l(M). The result (i) yields an affirmative answer to the question, open for some time, of whether the support of a stable probability measure of index 1 less-than-or-equal-to alpha < 2 on B is a translate of a linear space. Analogs of these results, for both Poisson and stable probability measures defined on general locally convex spaces, are also provided.
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