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We consider a Markov chain with a general state space, but whose behavior is governed by finite matrices. After a brief exposition of the basic properties of this chain, its convenience as a model is illustrated by three limit theorems. The ergodic theorem, the central limit theorem, and an extreme-value theorem are expressed in terms of dominant eigenvalues of finite matrices and proved by simple matrix theory. 相似文献
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Simple conditions are given which characterize the generating function of a nonnegative multivariate infinitely divisible random vector. Necessary conditions on marginals, linear combinations, tail behavior, and zeroes are discussed, and a sufficient condition is given. The latter condition, which is a multivariate generalization of ordinary log-convexity, is shown to characterize only certain products of univariate infinitely divisible distributions. 相似文献
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We introduce an increasing set of classes Γa (0?α?1) of infinitely divisible (i.d.) distributions on {0,1,2,…}, such that Γ0 is the set of all compound-geometric distributions and Γ1 the set of all compound-Poisson distributions, i.e. the set of all i.d. distributions on the non-negative integers. These classes are defined by recursion relations similar to those introduced by Katti [4] for Γ1 and by Steutel [7] for Γ0. These relations can be regarded as generalizations of those defining the so-called renewal sequences (cf. [5] and [2]). Several properties of i.d. distributions now appear as special cases of properties of the Γa'. 相似文献
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Rampf E Schröder U de Wette FW Kulkarni AD Kress W 《Physical review. B, Condensed matter》1993,48(14):10143-10152
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