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The Itô Integral with respect to an Infinite Dimensional Lévy Process: A Series Approach

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  • Stefan Tappe

Abstract

We present an alternative construction of the infinite dimensional Itô integral with respect to a Hilbert space valued Lévy process. This approach is based on the well-known theory of real-valued stochastic integration, and the respective Itô integral is given by a series of Itô integrals with respect to standard Lévy processes. We also prove that this stochastic integral coincides with the Itô integral that has been developed in the literature.

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  • Stefan Tappe, 2013. "The Itô Integral with respect to an Infinite Dimensional Lévy Process: A Series Approach," International Journal of Stochastic Analysis, Hindawi, vol. 2013, pages 1-14, April.
    • Handle: RePEc:hin:jnijsa:703769
    DOI: 10.1155/2013/703769
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