The Itô integral with respect to an infinite dimensional Lévy process: A series approach
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arXiv
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866914164984774656 |
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| author | Tappe, Stefan |
| author_facet | Tappe, Stefan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1907_01450 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | The Itô integral with respect to an infinite dimensional Lévy process: A series approach Tappe, Stefan Probability Functional Analysis 60H05, 60G51 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. |
| title | The Itô integral with respect to an infinite dimensional Lévy process: A series approach |
| topic | Probability Functional Analysis 60H05, 60G51 |
| url | https://arxiv.org/abs/1907.01450 |