Operator-stable laws
| Autor: | J.David Mason, William N. Hudson |
|---|---|
| Rok vydání: | 1981 |
| Předmět: |
Unit sphere
Statistics and Probability Numerical Analysis Operator (physics) Gaussian Mathematical analysis central limit theorem multivariate stable laws Measure (mathematics) Linear subspace symbols.namesake Covariance operator Operator-stable distributions symbols Exponent Statistics Probability and Uncertainty Central limit theorem Mathematics |
| Zdroj: | Journal of Multivariate Analysis. 11(3):434-447 |
| ISSN: | 0047-259X |
| DOI: | 10.1016/0047-259x(81)90086-5 |
| Popis: | Sharpe investigated the structure of full operator-stable measures μ on a vector group V and obtained decompositions, μ = μ1 ∗ μ2 and V = V1 ⊕ V2, in terms of the Gaussian component μ1 and the Poisson component μ2. The subspaces V1 and V2 are here identified in terms of an exponent B for μ. Sharpe also pointed out that the Lévy measure M of μ is a mixture of Lévy measures concentrated on single orbits of tB. Here, an explicit representation is obtained for M as such a mixture by constructing a measure on the unit sphere. Also, necessary and sufficient conditions are given that a Lévy measure be the Lévy measure of a full operator-stable measure. The final result deals with full Gaussian measures μ and establishes the connection between its covariance operator and the class of all exponents of μ. |
| Databáze: | OpenAIRE |
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