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Density Estimate in Small Time for Jump Processes with Singular Lévy Measures

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Stochastic Analysis and Related Topics VII

Part of the book series: Progress in Probability ((PRPR,volume 48))

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Abstract

In this chapter, we study the asymptotic behavior of the transition density for processes of jump type as the time parameter t tends to 0. We use Picard’s duality method, which allows us to obtain the lower and upper bounds of the density even for the case where the support of Lévy measure is very singular.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, Ehime University, Matsuyama, Japan

    Y. Ishikawa

Authors
  1. Y. Ishikawa
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Editor information

Editors and Affiliations

  1. Département Réseaux, Ecole Nationale Supérieure des Télécommunications, Paris Cedex 13, 75634, France

    Laurent Decreusefond  & Ali Süleyman Üstünel  & 

  2. Department of Mathematics, University of Oslo, N-0316, Oslo, Norway

    Bernt K. Øksendal

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© 2001 Springer Science+Business Media New York

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Ishikawa, Y. (2001). Density Estimate in Small Time for Jump Processes with Singular Lévy Measures. In: Decreusefond, L., Øksendal, B.K., Üstünel, A.S. (eds) Stochastic Analysis and Related Topics VII. Progress in Probability, vol 48. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0157-1_8

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  • DOI: https://doi.org/10.1007/978-1-4612-0157-1_8

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  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6638-9

  • Online ISBN: 978-1-4612-0157-1

  • eBook Packages: Springer Book Archive

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