Sil’vestrov, D. S.; Abadov, Z. A. Uniform representations of exponential moments of sums of random variables defined on a Markov chain, and of distributions of passage times. I. (English. Russian original) Zbl 0834.60085 Theory Probab. Math. Stat. 45, 105-120 (1992); translation from Teor. Veroyatn. Mat. Stat., Kiev 45, 108-127 (1991). Summary: Asymptotic representations uniform with respect to a series parameter are obtained for exponential moments of sums of random variables defined on a Markov chain, with an explicit estimate of the remainder terms. Cited in 1 ReviewCited in 1 Document MSC: 60J27 Continuous-time Markov processes on discrete state spaces 60G50 Sums of independent random variables; random walks Keywords:asymptotic representations; exponential moments; explicit estimate of the remainder terms PDFBibTeX XMLCite \textit{D. S. Sil'vestrov} and \textit{Z. A. Abadov}, Theory Probab. Math. Stat. 45, 1 (1991; Zbl 0834.60085); translation from Teor. Veroyatn. Mat. Stat., Kiev 45, 108--127 (1991)