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arXiv · 1907.01450

The It\^{o} integral with respect to an infinite dimensional L\'{e}vy process: A series approach

Stefan Tappe
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Abstract

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

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Stefan Tappe. 2019-07-02. The It\^{o} integral with respect to an infinite dimensional L\'{e}vy process: A series approach. https://doi.org/10.1155/2013%2F703769

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