Silvestrov, D. S. Exponential asymptotic for a perturbed renewal equation. (English. Ukrainian original) Zbl 0946.60080 Theory Probab. Math. Stat. 52, 153-162 (1996); translation from Teor. Jmovirn. Mat. Stat. 52, 143-153 (1995). New types of the exponential asymptotic expansions for solutions of the disturbed renewal equation are obtained. Some ergodic theorems and limit theorems on the convergence in distribution of the functionals of stopping times for regenerating processes are generalized. These theorems include both the theorem on the convergence in distribution and the large deviations theorem. Reviewer: A.V.Swishchuk (Kyïv) Cited in 1 ReviewCited in 8 Documents MSC: 60K05 Renewal theory 60F17 Functional limit theorems; invariance principles 60K15 Markov renewal processes, semi-Markov processes Keywords:renewal equation; exponential asymptotic; stopping time PDFBibTeX XMLCite \textit{D. S. Silvestrov}, Teor. Ĭmovirn. Mat. Stat. 52, 143--153 (1995; Zbl 0946.60080); translation from Teor. Jmovirn. Mat. Stat. 52, 143--153 (1995)