Classical solution of path-dependent mean-field semilinear PDEs
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
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| _version_ | 1866909267011829760 |
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| author | Tang, Shanjian Zhang, Huilin |
| author_facet | Tang, Shanjian Zhang, Huilin |
| contents | The paper concerns classical solution of path-dependent partial differential equations (PPDEs) with coefficients depending on both variables of path and path-valued measure, which are crucial to understanding large-scale mean-field interacting systems in a non-Markovian setting. We construct classical solutions of the PPDEs via solution of the forward and backward stochastic differential equations. To accommodate the intricacies introduced by the appearance of the path in the coefficients, we develop a novel technique known as the ``parameter frozen'' approach to the PPDEs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_05282 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Classical solution of path-dependent mean-field semilinear PDEs Tang, Shanjian Zhang, Huilin Probability Optimization and Control 60G22, 60H10, 34C29 The paper concerns classical solution of path-dependent partial differential equations (PPDEs) with coefficients depending on both variables of path and path-valued measure, which are crucial to understanding large-scale mean-field interacting systems in a non-Markovian setting. We construct classical solutions of the PPDEs via solution of the forward and backward stochastic differential equations. To accommodate the intricacies introduced by the appearance of the path in the coefficients, we develop a novel technique known as the ``parameter frozen'' approach to the PPDEs. |
| title | Classical solution of path-dependent mean-field semilinear PDEs |
| topic | Probability Optimization and Control 60G22, 60H10, 34C29 |
| url | https://arxiv.org/abs/2109.05282 |