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Teor. Veroyatnost. i Primenen., 2008, Volume 53, Issue 2, Pages 349–353 (Mi tvp2414)  

This article is cited in 1 scientific paper (total in 1 paper)

Short Communications

An Extension of the Ocone–Haussmann–Clark Formula for the Compensated Poisson Processes

V. Jaoshvili, O. G. Purtukhiya

Tbilisi Ivane Javakhishvili State University

Abstract: The Sobolev-type spaces $D_{p,1,\alpha }^{CP}$ ($1\le p\le2$) are defined for the compensated Poisson process, and the stochastic integral representation (analogous to the Ocone–Haussmann–Clark formula) is derived for the functionals from these spaces. The formula is given for the computation of the predictable projections of the stochastic derivatives of the above-mentioned functionals.

Keywords: Ocone–Haussmann–Clark formula, compensated Poisson process, stochastic derivative, predictable projection.

DOI: https://doi.org/10.4213/tvp2414

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English version:
Theory of Probability and its Applications, 2009, 53:2, 316–321

Bibliographic databases:

Received: 21.08.2007

Citation: V. Jaoshvili, O. G. Purtukhiya, “An Extension of the Ocone–Haussmann–Clark Formula for the Compensated Poisson Processes”, Teor. Veroyatnost. i Primenen., 53:2 (2008), 349–353; Theory Probab. Appl., 53:2 (2009), 316–321

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Purtukhia O., Jaoshvili V., “Sobolev–Poincaré Type Inequalities for Poisson Functionals”, 2012 IV International Conference Problems of Cybernetics and Informatics (PCI), ed. AidaZade K., IEEE, 2012  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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