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On fully coupled continuous time random walks. (English) Zbl 1237.60038

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.

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
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