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Martingale Representations for Functionals of Lévy Processes

Abstract

We describe the integrand in the martingale (or stochastic integral) representation of a square integrable functional F of a Lévy process in terms of (a derivative or difference operator acting on) a map ß F introduced in Rajeev and Fitzsimmons (Stochastics 81, 467–476, 2009). The kernels in the chaos expansion of F are also described in terms of the iterated derivative and difference operators.

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Correspondence to B. Rajeev.

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Rajeev, B. Martingale Representations for Functionals of Lévy Processes. Sankhya A 77, 277–299 (2015). https://doi.org/10.1007/s13171-015-0073-8

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  • DOI: https://doi.org/10.1007/s13171-015-0073-8

Keywords and phrases

  • Martingale representation
  • Stochastic integral representation
  • Lévy processes
  • Chaos expansion
  • Stochastic derivative

AMS (2000) subject classification

  • Primary 60H10
  • 60H15
  • Secondary 60J60
  • 35K15