Stochastic sewing lemma on Wasserstein space
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915043590799360 |
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| author | Alfonsi, Aurélien Bally, Vlad Caramellino, Lucia |
| author_facet | Alfonsi, Aurélien Bally, Vlad Caramellino, Lucia |
| contents | The stochastic sewing lemma recently introduced by Le~(2020) allows to construct a unique limit process from a doubly indexed stochastic process that satisfies some regularity. This lemma is stated in a given probability space on which these processes are defined. The present paper develops a version of this lemma for probability measures: from a doubly indexed family of maps on the set of probability measures that have a suitable probabilistic representation, we are able to construct a limit flow of maps on the probability measures. This result complements and improves the existing result coming from the classical sewing lemma. It is applied to the case of law-dependent jump SDEs for which we obtain weak existence result as well as the uniqueness of the marginal laws. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17096 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stochastic sewing lemma on Wasserstein space Alfonsi, Aurélien Bally, Vlad Caramellino, Lucia Probability G0H20, 35Q83, 60L30 The stochastic sewing lemma recently introduced by Le~(2020) allows to construct a unique limit process from a doubly indexed stochastic process that satisfies some regularity. This lemma is stated in a given probability space on which these processes are defined. The present paper develops a version of this lemma for probability measures: from a doubly indexed family of maps on the set of probability measures that have a suitable probabilistic representation, we are able to construct a limit flow of maps on the probability measures. This result complements and improves the existing result coming from the classical sewing lemma. It is applied to the case of law-dependent jump SDEs for which we obtain weak existence result as well as the uniqueness of the marginal laws. |
| title | Stochastic sewing lemma on Wasserstein space |
| topic | Probability G0H20, 35Q83, 60L30 |
| url | https://arxiv.org/abs/2410.17096 |