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Multivariate subordination, self-decomposability and stability
Advances in Applied Probability, 2001Multivariate subordinators are multivariate Lévy processes that are increasing in each component. Various examples of multivariate subordinators, of interest for applications, are given. Subordination of Lévy processes with independent components by multivariate subordinators is defined.
Barndorff-Nielsen, O.E. +2 more
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Natural exponential families and self-decomposability
Statistics & Probability Letters, 1992zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bar-Lev, Shaul K. +2 more
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Completeness and self-decomposability of mixtures
Annals of the Institute of Statistical Mathematics, 1983A family \(\{P_{\theta}\), \(\theta\in \Theta \}\) of probability distributions is defined to be strongly complete if \(E_{\theta}[g(X)]=0\) for all \(\theta\) in a dense subset of \(\Theta\) implies that \(g(X)=0\) a.s. \((P_{\theta})\) for all \(\theta\in \Theta\). Obviously exponential families (of standard type) are strongly complete.
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Two Novel Characterizations of Self-Decomposability on the Half-Line
Journal of Theoretical Probability, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mai, Jan-Frederik +2 more
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Supremum self-decomposable random vectors
Probability Theory and Related Fields, 1986An \({\bar {\mathbb{R}}}^ d\)-valued random variable X is said to be sup selfdecomposable if for each \(t>0\) there is an \({\bar {\mathbb{R}}}^ d\)- valued random variable \(X_ t\) independent of X such that \[ (1)\quad X=^{d}(X-t\cdot 1)\vee X_ t, \] where \(=^{d}\) means equality in distribution and \(\vee\) means componentwise supremum.
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Semi-self-decomposable distributions on Z+
Annals of the Institute of Statistical Mathematics, 2007We present a notion of semi-self-decomposability for distributions with support in Z+. We show that discrete semi-self-decomposable distributions are infinitely divisible and are characterized by the absolute monotonicity of a specific function. The class of discrete semi-self-decomposable distributions is shown to contain the discrete semistable ...
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Self-decomposable discrete distributions and branching processes
Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1981Self-decomposable distributions are known to be absolutely continuous. In this note analogues of the concept of self-decomposability are proposed for distributions on the set ℕ0 of nonnegative integers. To each of them corresponds an analogue of multiplication (in distribution) that preserves ℕ0-valuedness and is characterized by a composition ...
Harn, van, K. +2 more
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Probability and Statistics: Self-Decomposability, Finance and Turbulence
1998After some general remarks about the relationship between probability and statistics, a discussion is given of closely similar, key features of empirical data from finance and from turbulence, and this is followed by an account of recent work on stochastic modelling incorporating those features.
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Self decomposability and option pricing
2007The risk-neutral process is modeled by a four parameter self-similar process of independent increments with a self-decomposable law for its unit time distribution. Six different processes in this general class are theoretically formulated and empirically investigated.
Geman, Helyette +1 more
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Self-decomposability on ℝ and ℤ
1984The set L(ℝ) of self-decomposable probability measures on ℝ is studied in terms of characteristic functions using a certain differential operator and its inverse. In particular a natural bijection onto L(ℝ), introduced by Wolfe, is interpreted via these operators.
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