共查询到20条相似文献,搜索用时 9 毫秒
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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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D. Mejzler 《Israel Journal of Mathematics》1973,16(1):1-19
We characterize the class of distribution functions Φ(x), which are limits in the following sense: there exist a sequence of independent and equally distributed random variables {ξ n }, numerical sequences {a k }, {b k } and natural numbers {n k } such that $$\mathop {lim}\limits_{k \to \infty } Prob\left\{ {\frac{1}{{a_k }}\mathop {\Sigma }\limits_{k = 1}^{n_k } \xi _k - b_k< x} \right\} = \Phi (x)$$ and $$\mathop {\lim \inf }\limits_{k \to \infty } (n_k /n_{k + 1} ) > 0$$ . 相似文献
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M. S. Sgibnev 《Mathematical Notes》1989,46(4):794-798
Translated from Matematicheskie Zametki, Vol. 46, No. 4, pp. 60–65, October, 1989. 相似文献
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R.C Griffiths 《Journal of multivariate analysis》1984,15(1):13-20
A particular class of p-dimensional exponential distributions have Laplace transforms |I + VT|?1, V positive definite or positive semi-definite and T = diagonal (t1,…, tp). A characterization is given of when these Laplace transforms are infinitely divisible. 相似文献
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A. L. Yakymiv 《Journal of Mathematical Sciences》1997,84(3):1197-1207
The present article deals with the asymptotics at infinity of multidimensional infinitely divisible distributions with the
support in a cone.
Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russian, 1995, Part III. 相似文献
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《Stochastic Processes and their Applications》2005,115(5):737-768
We obtain new conditions for partial sums of an array with stationary rows to converge to a mixture of infinitely divisible distributions with finite variance. More precisely, we show that these conditions are necessary and sufficient to obtain conditional convergence. If the underlying -algebras are nested, conditional convergence implies stable convergence in the sense of Rényi. From this general result we derive new criteria expressed in terms of conditional expectations, which can be checked for many processes such as m-conditionally centered arrays or mixing arrays. When it is relevant, we establish the weak convergence of partial sum processes to a mixture of Lévy processes in the space of cadlag functions equipped with Skorohod's topology. The cases of Wiener processes, Poisson processes and Bernoulli distributed variables are studied in detail. 相似文献
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Stricker’s theorem states that a Gaussian process is a semimartingale in its natural filtration if and only if it is the sum of an independent increment Gaussian process and a Gaussian process of finite variation, see Stricker (Z Wahrsch Verw Geb 64(3):303–312, 1983). We consider extensions of this result to non Gaussian infinitely divisible processes. First we show that the class of infinitely divisible semimartingales is so large that the natural analog of Stricker’s theorem fails to hold. Then, as the main result, we prove that an infinitely divisible semimartingale relative to the filtration generated by a random measure admits a unique decomposition into an independent increment process and an infinitely divisible process of finite variation. Consequently, the natural analog of Stricker’s theorem holds for all strictly representable processes (as defined in this paper). Since Gaussian processes are strictly representable due to Hida’s multiplicity theorem, the classical Stricker’s theorem follows from our result. Another consequence is that the question when an infinitely divisible process is a semimartingale can often be reduced to a path property, when a certain associated infinitely divisible process is of finite variation. This gives the key to characterize the semimartingale property for many processes of interest. Along these lines, using Basse-O’Connor and Rosiński (Stoch Process Appl 123(6):1871–1890, 2013a), we characterize semimartingales within a large class of stationary increment infinitely divisible processes; this class includes many infinitely divisible processes of interest, including linear fractional processes, mixed moving averages, and supOU processes, as particular cases. The proof of the main theorem relies on series representations of jumps of càdlàg infinitely divisible processes given in Basse-O’Connor and Rosiński (Ann Probab 41(6):4317–4341, 2013b) combined with techniques of stochastic analysis. 相似文献
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David Berger 《Mathematische Nachrichten》2019,292(8):1674-1684
An infinitely divisible distribution on is a probability measure μ such that the characteristic function has a Lévy–Khintchine representation with characteristic triplet , where ν is a Lévy measure, and . A natural extension of such distributions are quasi‐infinitely distributions. Instead of a Lévy measure, we assume that ν is a “signed Lévy measure”, for further information on the definition see [10]. We show that a distribution with and , where is the absolutely continuous part, is quasi‐infinitely divisible if and only if for every . We apply this to show that certain variance mixtures of mean zero normal distributions are quasi‐infinitely divisible distributions, and we give an example of a quasi‐infinitely divisible distribution that is not continuous but has infinite quasi‐Lévy measure. Furthermore, it is shown that replacing the signed Lévy measure by a seemingly more general complex Lévy measure does not lead to new distributions. Last but not least it is proven that the class of quasi‐infinitely divisible distributions is not open, but path‐connected in the space of probability measures with the Prokhorov metric. 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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Michael Braverman 《Statistics & probability letters》2011,81(11):1648-1653
We show that if the tail of a Lévy measure is light, then the same holds for the tail of the corresponding infinitely divisible distribution. 相似文献