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A different quantum stochastic calculus for the Poisson process
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  • Published: June 1996

A different quantum stochastic calculus for the Poisson process

  • Nicolas Privault1 

Probability Theory and Related Fields volume 105, pages 255–278 (1996)Cite this article

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  • 7 Citations

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Summary

We show that a gradient operator defined by perturbations of the Poisson process jump times can be used with its adjoint operator instead of the annihilation and creation operators on the Poisson-Charlier chaotic decomposition to represent the Poisson process. The quantum stochastic integration and the Itô formula are developed accordingly, leading to commutation relations which are different from the CCR. An analog of the Weyl representation is defined for a subgroup ofSL(2, ℝ), showing that the exponential and geometric distributions are closely related in this approach.

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Authors and Affiliations

  1. Equipe d'Analyse et Probabilités, Université d'Evry-Val d'Essonne, Boulevard des Coquibus, F-91025, Evry Cedex, France

    Nicolas Privault

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  1. Nicolas Privault
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Privault, N. A different quantum stochastic calculus for the Poisson process. Probab. Th. Rel. Fields 105, 255–278 (1996). https://doi.org/10.1007/BF01203837

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  • Received: 07 August 1995

  • Revised: 07 February 1996

  • Issue Date: June 1996

  • DOI: https://doi.org/10.1007/BF01203837

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Mathematics Subject Classification (1991)

  • 81S25
  • 60H07
  • 60G55
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