Stochastic integration with respect to cylindrical Lévy processes in Hilbert spaces
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913266665521152 |
|---|---|
| author | Bodó, Gergely Riedle, Markus |
| author_facet | Bodó, Gergely Riedle, Markus |
| contents | In this work, we present a comprehensive theory of stochastic integration with respect to arbitrary cylindrical Lévy processes in Hilbert spaces. Since cylindrical Lévy processes do not enjoy a semi-martingale decomposition, our approach relies on an alternative approach to stochastic integration by decoupled tangent sequences. The space of deterministic integrands is identified as a modular space described in terms of the characteristics of the cylindrical Lévy process. The space of random integrands is described as the space of predictable processes whose trajectories are in the space of deterministic integrands almost surely. The derived space of random integrands is verified as the largest space of potential integrands, based on a classical definition of stochastic integrability. We apply the introduced theory of stochastic integration to establish a dominated convergence theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_10453 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stochastic integration with respect to cylindrical Lévy processes in Hilbert spaces Bodó, Gergely Riedle, Markus Probability 60H05, 60G20, 60G51, 28C20 In this work, we present a comprehensive theory of stochastic integration with respect to arbitrary cylindrical Lévy processes in Hilbert spaces. Since cylindrical Lévy processes do not enjoy a semi-martingale decomposition, our approach relies on an alternative approach to stochastic integration by decoupled tangent sequences. The space of deterministic integrands is identified as a modular space described in terms of the characteristics of the cylindrical Lévy process. The space of random integrands is described as the space of predictable processes whose trajectories are in the space of deterministic integrands almost surely. The derived space of random integrands is verified as the largest space of potential integrands, based on a classical definition of stochastic integrability. We apply the introduced theory of stochastic integration to establish a dominated convergence theorem. |
| title | Stochastic integration with respect to cylindrical Lévy processes in Hilbert spaces |
| topic | Probability 60H05, 60G20, 60G51, 28C20 |
| url | https://arxiv.org/abs/2403.10453 |