Boundedness of the norm density of a stable random vector in Hilbert space. (Russian) Zbl 0629.60009

Pap, D.

Teor. Veroyatn. Mat. Stat., Kiev 36, 102-105 (1987).

The author shows that the density of the distribution of the norm of a symmetric p-stable random vector, \(1<p<2\), in a separable Hilbert space is bounded. The proof is based on the series representation of p-stable vectors as a mixture of Gaussian vectors, obtained first by R. Le Page, M. Woodroofe and J. Zinn [Ann. Probab. 9, 624-632 (1981; Zbl 0465.60031)].
Reviewer’s remark: This result for all \(0<p<2\) has been proved by T. Żak (Probability Math. Stat. to appear). For the related results on the asymptotic behaviour of the density at infinity for \(0<p<1\) see also M. Lewandowski and T. Żak, Proc. Am. Math. Soc. 100, 345- 351 (1987).

Reviewer: A.E.Weron

MSC:

60B05	Probability measures on topological spaces
60E07	Infinitely divisible distributions; stable distributions

Keywords:

p-stable random vector; mixture of Gaussian vectors; asymptotic behaviour of the density at infinity

Citations:

Zbl 0465.60031