Korolyuk, V. S.; Limnios, N. Poisson approximation of homogeneous additive stochastic functionals with semi-Markov switchings. (English. Ukrainian original) Zbl 0998.60028 Theory Probab. Math. Stat. 64, 75-84 (2002); translation from Teor. Jmovirn. Mat. Stat. 64, 66-74 (2001). The authors prove a number of weak convergence results for the additive jump functionals with semi-Markov switching in the scheme of Poisson approximation depending on a small parameter. Reviewer: N.M.Zinchenko (Kyïv) Cited in 1 Document MSC: 60F17 Functional limit theorems; invariance principles 60J35 Transition functions, generators and resolvents Keywords:semi-Markov process; Markov process; additive functional; semimartingale; compensator; predictable characteristic; characterization PDFBibTeX XMLCite \textit{V. S. Korolyuk} and \textit{N. Limnios}, Teor. Ĭmovirn. Mat. Stat. 64, 66--74 (2001; Zbl 0998.60028); translation from Teor. Jmovirn. Mat. Stat. 64, 66--74 (2001)