caa a22 4500 60551948X CHVBK 20210128100730.0 cr unu---uuuuu 210128e20150301xx s 000 0 eng 10.1007/s11009-013-9350-y doi (NATIONALLICENCE)springer-10.1007/s11009-013-9350-y Zinchenko Nadiia Department of Informatics and Applied Mathematics, Nizhyn State Mukola Gogol University, 16600, Nizhyn, Ukraine aut Almost Sure Approximation of the Superposition of the Random Processes [Elektronische Daten] [Nadiia Zinchenko] This article presents sufficient conditions, which provide almost sure (a.s.) approximation of the superposition of the random processes S(N(t)), when càd-làg random processes S(t) and N(t) themselves admit a.s. approximation by a Wiener or stable Lévy processes. Such results serve as a source of numerous strong limit theorems for the random sums under various assumptions on counting process N(t) and summands. As a consequence we obtain a number of results concerning the a.s. approximation of the Kesten-Spitzer random walk, accumulated workload input into queuing system, risk processes in the classical and renewal risk models with small and large claims and use such results for investigation the growth rate and fluctuations of the mentioned processes. Springer Science+Business Media New York, 2013 Strong invariance principle nationallicence Superposition of random processes nationallicence Randomly stopped sums nationallicence Queuing system nationallicence Risk process nationallicence Total claim amount nationallicence Stable process nationallicence Methodology and Computing in Applied Probability Springer US; http://www.springer-ny.com 17/1(2015-03-01), 235-250 1387-5841 17:1<235 2015 17 11009 https://doi.org/10.1007/s11009-013-9350-y text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s11009-013-9350-y text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Zinchenko Nadiia Department of Informatics and Applied Mathematics, Nizhyn State Mukola Gogol University, 16600, Nizhyn, Ukraine aut NATIONALLICENCE 773 0- Methodology and Computing in Applied Probability Springer US; http://www.springer-ny.com 17/1(2015-03-01), 235-250 1387-5841 17:1<235 2015 17 11009