On the asymptotic behavior of increments of certain classes of random fields. (English. Ukrainian original) Zbl 0840.60045

Zinchenko, N. M.

Theory Probab. Math. Stat. 48, 7-11 (1994); translation from Teor. Jmovirn. Mat. Stat. 48, 11-18 (1993).

Summary: Some integral criteria are proposed for studying the rate of growth of increments of stable fields with parameters \(\beta = 1\) and \(1 < \alpha \leq 2\) on rectangles \(Q\) of area \(\mu (Q) \leq a_T\), when \(a_T\) increases (but no faster than \(T)\) and \(Q\) belongs to a region \(D_T\) of a special form on a plane. In particular, certain criteria for the 2-parameter Brownian motion are considered. Some generalizations to the case of \(n\)-dimensional parameter are obtained.

MSC:

60G60	Random fields
60J99	Markov processes
60F15	Strong limit theorems

Keywords:

stable random fields; asymptotic; rate of growth of increments of stable fields; two-parameter Brownian motion