Cylindrical Martingale-Valued Measures, Stochastic Integration and SPDEs
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913892788076544 |
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| author | Cambronero, Santiago Campos, David Fonseca-Mora, C. A. Mena, Darío |
| author_facet | Cambronero, Santiago Campos, David Fonseca-Mora, C. A. Mena, Darío |
| contents | We develop a theory of Hilbert-space valued stochastic integration with respect to cylindrical martingale-valued measures. As part of our construction, we expand the concept of quadratic variation, introduced by Veraar and Yaroslavtsev (2016), to the case of cylindrical martingale-valued measures that are allowed to have discontinuous paths (this is carried out within the context of separable Banach spaces). Our theory of stochastic integration is applied to address the existence and uniqueness of solutions to stochastic partial differential equations in Hilbert spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_10374 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cylindrical Martingale-Valued Measures, Stochastic Integration and SPDEs Cambronero, Santiago Campos, David Fonseca-Mora, C. A. Mena, Darío Probability Functional Analysis 60H05, 60H15, 60B11, 60G48 We develop a theory of Hilbert-space valued stochastic integration with respect to cylindrical martingale-valued measures. As part of our construction, we expand the concept of quadratic variation, introduced by Veraar and Yaroslavtsev (2016), to the case of cylindrical martingale-valued measures that are allowed to have discontinuous paths (this is carried out within the context of separable Banach spaces). Our theory of stochastic integration is applied to address the existence and uniqueness of solutions to stochastic partial differential equations in Hilbert spaces. |
| title | Cylindrical Martingale-Valued Measures, Stochastic Integration and SPDEs |
| topic | Probability Functional Analysis 60H05, 60H15, 60B11, 60G48 |
| url | https://arxiv.org/abs/2308.10374 |