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Compound Poisson processes: Potentials, Green measures and random times

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  • Kondratiev, Yuri
  • da Silva, José L.

Abstract

In this paper we study the existence of Green measures for Markov processes with a nonlocal jump generator. The non-singular jump kernel has no second moment and satisfies a suitable condition on its Fourier transform. We also study the same problem for certain classes of random time changes Markov processes with jump generator.

Suggested Citation

  • Kondratiev, Yuri & da Silva, José L., 2023. "Compound Poisson processes: Potentials, Green measures and random times," Statistics & Probability Letters, Elsevier, vol. 197(C).
    • Handle: RePEc:eee:stapro:v:197:y:2023:i:c:s0167715223000391
    DOI: 10.1016/j.spl.2023.109815
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    References listed on IDEAS

    as
    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. Mura, A. & Taqqu, M.S. & Mainardi, F., 2008. "Non-Markovian diffusion equations and processes: Analysis and simulations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(21), pages 5033-5064.
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