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Smoothness of harmonic functions for processes with jumps

Author

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  • Picard, Jean
  • Savona, Catherine

Abstract

We consider a non-local operator L associated to a Markov process with jumps, we stop this process when it quits a domain D, and we study the Cj smoothness on D of the functions which are harmonic for the stopped process. A previous work was devoted to the existence of a C[infinity] transition density; here, the smoothness of harmonic functions is deduced by applying a duality method and by estimating the density in small time.

Suggested Citation

  • Picard, Jean & Savona, Catherine, 2000. "Smoothness of harmonic functions for processes with jumps," Stochastic Processes and their Applications, Elsevier, vol. 87(1), pages 69-91, May.
    • Handle: RePEc:eee:spapps:v:87:y:2000:i:1:p:69-91
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    References listed on IDEAS

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    1. Picard, Jean, 1997. "Density in small time at accessible points for jump processes," Stochastic Processes and their Applications, Elsevier, vol. 67(2), pages 251-279, May.
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    Cited by:

    1. Brice Franke, 2007. "A Functional Non-Central Limit Theorem for Jump-Diffusions with Periodic Coefficients Driven by Stable Lévy-Noise," Journal of Theoretical Probability, Springer, vol. 20(4), pages 1087-1100, December.

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