On multidimensional Mandelbrot cascades
| Autor: | Dariusz Buraczewski, Yves Guivarc'h, Ewa Damek, Sebastian Mentemeier |
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| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | Journal of Difference Equations and Applications. 20:1523-1567 |
| ISSN: | 1563-5120 1023-6198 |
| DOI: | 10.1080/10236198.2014.950259 |
| Popis: | Let Z be a random variable with values in a proper closed convex cone , A a random endomorphism of C and N a random integer. We assume that Z, A, N are independent. Given N independent copies of we define a new random variable . Let T be the corresponding transformation on the set of probability measures on C, i.e. T maps the law of Z to the law of . If the matrix has dominant eigenvalue 1, we study existence and properties of fixed points of T having finite non-zero expectation. Existing one-dimensional results concerning T are extended to higher dimensions. In particular we give conditions under which such fixed points of T have multidimensional regular variation in the sense of extreme value theory and we determine the index of regular variation. |
| Databáze: | OpenAIRE |
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