Zum asymptotischen Verhalten der Verteilungen und der Dichten gewisser Funktionale Gauß’scher Zufallsvektoren. (On the asymptotic behaviour of the distributions and densities of certain functionals of Gaussian random vectors). (German) Zbl 0653.60026
Let \(h_ A\) denote a Minkowski-functional of an element A from a certain class of finite-dimensional and not necessarily convex Borel sets and put \(f(x)=\Phi (\{z\in R^ k:\) \(h_ A(z)\leq x\})\), \(x>0\), where \(\Phi\) denotes the standard Gaussian distribution. Under some “geometric” assumptions on A the asymptotic behaviour of f and its derivative are discussed for \(x\to \infty\) and \(x\to 0\).
Reviewer: W.-D.Richter
MSC:
| 60F10 | Large deviations |
References:
| [1] | Hertle, Lect. Notes Math. 990 pp 221– (1983) |
| [2] | [Russian Text Ignored.] 21 pp 4– (1976) |
| [3] | On the density of the norm Gaussian vector in Banach spaces. Lect. Notes Math. 990 (1983) 172–197 |
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| [7] | [Russian Text Ignored.] 20 pp 5– (1979) |
| [8] | [Russian Text Ignored.] 1971 |
| [9] | [Russian Text Ignored.] 6 pp 2– (1961) |
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