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Scaling limits of coupled continuous time random walks and residual order statistics through marked point processes

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  • Barczyk, A.
  • Kern, P.

Abstract

A continuous time random walk (CTRW) is a random walk in which both spatial changes represented by jumps and waiting times between the jumps are random. The CTRW is coupled if a jump and its preceding or following waiting time are dependent random variables (r.v.), respectively. The aim of this paper is to explain the occurrence of different limit processes for CTRWs with forward- or backward-coupling in Straka and Henry (2011) [37] using marked point processes. We also establish a series representation for the different limits. The methods used also allow us to solve an open problem concerning residual order statistics by LePage (1981) [20].

Suggested Citation

  • Barczyk, A. & Kern, P., 2013. "Scaling limits of coupled continuous time random walks and residual order statistics through marked point processes," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 796-812.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:3:p:796-812
    DOI: 10.1016/j.spa.2012.10.013
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    References listed on IDEAS

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    1. Meerschaert, Mark M. & Scheffler, Hans-Peter, 2008. "Triangular array limits for continuous time random walks," Stochastic Processes and their Applications, Elsevier, vol. 118(9), pages 1606-1633, September.
    2. Ward Whitt, 1980. "Some Useful Functions for Functional Limit Theorems," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 67-85, February.
    3. Straka, P. & Henry, B.I., 2011. "Lagging and leading coupled continuous time random walks, renewal times and their joint limits," Stochastic Processes and their Applications, Elsevier, vol. 121(2), pages 324-336, February.
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    Cited by:

    1. Scalas, Enrico & Viles, Noèlia, 2014. "A functional limit theorem for stochastic integrals driven by a time-changed symmetric α-stable Lévy process," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 385-410.

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