Some properties of asymptotic quasi-inverse functions and their applications. II. (Ukrainian, English) Zbl 1101.26003

Buldygin, V. V.; Klesov, O. I.; Steinebach, J. G.

Teor. Jmovirn. Mat. Stat. 71, 33-48 (2004); translation in Theory Probab. Math. Stat. 71, 37-52 (2005).

[For part I see ibid. 70, 9–25 (2004); resp. ibid. 70, 11–28 (2005; Zbl 1103.26001).]
The authors continue to study properties of functions, which are (quasi-)inverse to PRV and POV functions. For the POV functions the equivalence of all asymptotically quasi-inverse functions is proved. Conditions are obtained under which the limit behaviour of a ratio of quasi-inverse functions is determined by the asymptotic behaviour of the ratio of functions themselves. Applications to investigation of the asymptotic behaviour of solutions of stochastic differential equations and investigation of generalized renewal processes are presented.

Reviewer: A. D. Borisenko (Kyïv)

MSC:

26A12	Rate of growth of functions, orders of infinity, slowly varying functions
60F15	Strong limit theorems

Keywords:

PRV and POV functions; limit behaviour; ratio of quasi-inverse functions; generalized renewal processes

Citations:

Zbl 1103.26001