On sample properties of random fields with stable increments. (English. Russian original) Zbl 0836.60044

Bondarenko, I. V.; Ivanov, A. V.

Theory Probab. Math. Stat. 47, 9-13 (1993); translation from Teor. Jmovirn. Mat. Stat. 47, 11-15 (1992).

Summary: The quasinorms \(|\xi |_p=({\mathbf E} (|\xi |^p/(1 + |\xi |^p)) )^{1/p}\), \(p > 1\), for stable random variables with stability parameter \(\alpha\), \(0 < \alpha < 2\), are considered. Estimates for \(|\xi |_p\) in terms of the scale parameter of the stable distribution are obtained for certain relations between \(\alpha\) and \(p\). The estimates are used in the formulation of some assertions concerning the continuity of random fields with stable increments.

MSC:

60G17	Sample path properties
60G60	Random fields

Keywords:

stable distribution; random fields with stable increments