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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.15695 |
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| _version_ | 1866911817947676672 |
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| author | Jing, Guangdong Wang, Penghui Wang, Shan |
| author_facet | Jing, Guangdong Wang, Penghui Wang, Shan |
| contents | The main purpose of this paper is to obtain the existence and uniqueness of $L^p$-solution to quantum stochastic differential equation driven by Fermion fields with nonlocal conditions in the case of non-Lipschitz coefficients for $p>2$. The key to our technique is to make use of the Burkholder-Gundy inequality given by Pisier and Xu and Minkowski-type inequality to iterate instead of the fixed point theorem commonly used for nonlocal problems. Moreover, we also obtain the self-adjointness of the $L^p$-solution which is important in the study of optimal control problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_15695 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $L^p$-solutions of QSDE driven by Fermion fields with nonlocal conditions under non-Lipschitz coefficients Jing, Guangdong Wang, Penghui Wang, Shan Probability 46L51, 47J25, 60H10, 81S25 The main purpose of this paper is to obtain the existence and uniqueness of $L^p$-solution to quantum stochastic differential equation driven by Fermion fields with nonlocal conditions in the case of non-Lipschitz coefficients for $p>2$. The key to our technique is to make use of the Burkholder-Gundy inequality given by Pisier and Xu and Minkowski-type inequality to iterate instead of the fixed point theorem commonly used for nonlocal problems. Moreover, we also obtain the self-adjointness of the $L^p$-solution which is important in the study of optimal control problems. |
| title | $L^p$-solutions of QSDE driven by Fermion fields with nonlocal conditions under non-Lipschitz coefficients |
| topic | Probability 46L51, 47J25, 60H10, 81S25 |
| url | https://arxiv.org/abs/2403.15695 |