Szczotka, W.; Żebrowski, P. On fully coupled continuous time random walks. (English) Zbl 1237.60038 Appl. Math. 39, No. 1, 87-102 (2012). Summary: Continuous time random walks with jump sizes equal to the corresponding waiting times for jumps are considered. Sufficient conditions for the weak convergence of such processes are established and the limiting processes are identified. Furthermore one-dimensional distributions of the limiting processes are given under an additional assumption. Cited in 2 Documents MSC: 60G50 Sums of independent random variables; random walks 60E07 Infinitely divisible distributions; stable distributions 60F17 Functional limit theorems; invariance principles 60G51 Processes with independent increments; Lévy processes 60K05 Renewal theory Keywords:continuous time random walk; Lévy process; Lévy measure; Skorokhod topology PDFBibTeX XMLCite \textit{W. Szczotka} and \textit{P. Żebrowski}, Appl. Math. 39, No. 1, 87--102 (2012; Zbl 1237.60038) Full Text: DOI