Domains of attraction. The asymptotics of stochastic processes with independent increments. A survey of the work by B. V. Gnedenko and the generalizations. (English. Ukrainian original) Zbl 0926.60009

Zinchenko, N. M.

Theory Probab. Math. Stat. 56, 39-47 (1998); translation from Teor. Jmovirn. Mat. Stat. 56, 40-47 (1997).

A survey of results by B. V. Gnedenko and his students in the theory of attracting domains of stable distributions with further developments and applications is given. In particular, problems on attracting domains of the stable laws in \(R^{n},\) in Hilbert and Banach spaces and operator-stable measures are considered. The second part of the survey is devoted to the results by B. V. Gnedenko on local behaviour and rate of growth on the infinity of homogeneous random fields with independent increments and their generalizations.

Reviewer: A.V.Swishchuk (Kyïv)

MSC:

60-03	History of probability theory
60B12	Limit theorems for vector-valued random variables (infinite-dimensional case)
01A60	History of mathematics in the 20th century
60E07	Infinitely divisible distributions; stable distributions

Keywords:

attracting domains; stable laws; homogeneous random fields with independent increments