Invariance principles for renewal processes and some applications. (English. Ukrainian original) Zbl 0861.60045

Alex, M.; Steinebach, J.

Theory Probab. Math. Stat. 50, 23-54 (1995); translation from Teor. Jmovirn. Mat. Stat. 50, 22-54 (1994).

Summary: Excellent surveys on the development of invariance principles for partial sums, renewal processes, empirical and quantile processes have been given in the monographs of M. Csörgö and P. Révész [“Strong approximations in probability and statistics” (1981; Zbl 0539.60029)] and M. Csörgö and L. Horváth [“Weighted approximations in probability and statistics” (1993; Zbl 0770.60038)]. The aim of the present survey is to reflect the theory of invariance for renewal and related processes from a somewhat personal point of view. Recent results are discussed, which are not contained in the above-mentioned books, together with certain applications to queueing and risk models, to pontograms and their use in the change point analysis of renewal processes.

MSC:

60F17	Functional limit theorems; invariance principles
60F15	Strong limit theorems
60K05	Renewal theory
60K25	Queueing theory (aspects of probability theory)
62P05	Applications of statistics to actuarial sciences and financial mathematics

Keywords:

invariance principles; theory of invariance for renewal and related processes; pontograms

Citations:

Zbl 0539.60029; Zbl 0770.60038