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Integration by Parts for Poisson Processes

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  • Elliott, R. J.
  • Tsoi, A. H.

Abstract

Using a perturbation of the rate of a Poisson process and an inverse time change, an integration by parts formula is obtained. This enables a new form of the integrand in a martingale representation result to be obtained.

Suggested Citation

  • Elliott, R. J. & Tsoi, A. H., 1993. "Integration by Parts for Poisson Processes," Journal of Multivariate Analysis, Elsevier, vol. 44(2), pages 179-190, February.
    • Handle: RePEc:eee:jmvana:v:44:y:1993:i:2:p:179-190
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    Citations

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    Cited by:

    1. Privault, Nicolas, 2001. "Extended covariance identities and inequalities," Statistics & Probability Letters, Elsevier, vol. 55(3), pages 247-255, December.
    2. Murr, Rüdiger, 2013. "Characterization of infinite divisibility by duality formulas. Application to Lévy processes and random measures," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1729-1749.
    3. El-Khatib, Youssef & Abdulnasser, Hatemi-J, 2011. "On the calculation of price sensitivities with jump-diffusion structure," MPRA Paper 30596, University Library of Munich, Germany.
    4. Nicolas Privault & Anthony Réveillac, 2009. "Stein estimation of Poisson process intensities," Statistical Inference for Stochastic Processes, Springer, vol. 12(1), pages 37-53, February.
    5. Privault, N. & Yam, S.C.P. & Zhang, Z., 2019. "Poisson discretizations of Wiener functionals and Malliavin operators with Wasserstein estimates," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3376-3405.
    6. Takafumi Amaba, 2014. "A Discrete-Time Clark-Ocone Formula for Poisson Functionals," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 21(2), pages 97-120, May.
    7. Nicolas Privault, 2019. "Third Cumulant Stein Approximation for Poisson Stochastic Integrals," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1461-1481, September.
    8. Nicolas Privault, 2015. "Cumulant Operators for Lie–Wiener–Itô–Poisson Stochastic Integrals," Journal of Theoretical Probability, Springer, vol. 28(1), pages 269-298, March.
    9. Alexey M. Kulik, 2011. "Absolute Continuity and Convergence in Variation for Distributions of Functionals of Poisson Point Measure," Journal of Theoretical Probability, Springer, vol. 24(1), pages 1-38, March.

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