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Lagging and leading coupled continuous time random walks, renewal times and their joint limits

  • Straka, P.
  • Henry, B.I.
Registered author(s):

    Subordinating a random walk to a renewal process yields a continuous time random walk (CTRW), which models diffusion and anomalous diffusion. Transition densities of scaling limits of power law CTRWs have been shown to solve fractional Fokker-Planck equations. We consider limits of CTRWs which arise when both waiting times and jumps are taken from an infinitesimal triangular array. Two different limit processes are identified when waiting times precede jumps or follow jumps, respectively, together with two limit processes corresponding to the renewal times. We calculate the joint law of all four limit processes evaluated at a fixed time t.

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    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 121 (2011)
    Issue (Month): 2 (February)
    Pages: 324-336

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    Handle: RePEc:eee:spapps:v:121:y:2011:i:2:p:324-336
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    1. Mark M. Meerschaert & Enrico Scalas, 2006. "Coupled continuous time random walks in finance," Papers physics/0608281, arXiv.org.
    2. Scalas, Enrico & Gorenflo, Rudolf & Mainardi, Francesco, 2000. "Fractional calculus and continuous-time finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 376-384.
    3. Marco Raberto & Enrico Scalas & Francesco Mainardi, 2004. "Waiting-times and returns in high-frequency financial data: an empirical study," Finance 0411014, EconWPA.
    4. 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.
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