doi: 10.1685/journal.caim.483

Correlation Structure of Time-Changed Lévy Processes

Nikolai N Leonenko, Mark M Meerschaert, René L Schilling, Alla Sikorskii

Abstract


Time-Changed Lévy Processes include the fractional Poisson process, and the scaling limit of a continuous time random walk. They are obtained by replacing the deterministic time variable by a positive non-decreasing random process. The use of time-changed processes in modeling often requires the knowledge of their second order properties such as the correlation function. This paper provides the explicit expression for the correlation function for time-changed Lévy processes. The processes used to model random time include subordinators and inverse subordinators, and the time-changed Lévy processes include limits of continuous time random walks. Several examples useful in applications are discussed.

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Communications in Applied and Industrial Mathematics
ISSN: 2038-0909