Asymptotic behavior of renewal processes defined by random walks with multidimensional time. (English. Ukrainian original) Zbl 0923.60091

Klesov, Oleg I.; Steinebach, Josef G.

Theory Probab. Math. Stat. 56, 107-113 (1998); translation from Teor. Jmovirn. Mat. Stat. 56, 105-111 (1997).

One of the developed parts of the class of limit theorems in probability theory is the so-called renewal theory. The main problem of the renewal theory is to study the asymptotic behaviour as \(t\to +\infty\) of a renewal function or a renewal process with one-dimensional time. The authors discuss the problem of definition of a renewal process by a random walk with multidimensional time. They prove that the asymptotic behaviour of a renewal process depends on the dimension of indexes of a random walk.

Reviewer: A.V.Swishchuk (Kyïv)

MSC:

60K05	Renewal theory
60G50	Sums of independent random variables; random walks

Keywords:

renewal process; random walk; renewal theory