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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.12096 |
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| _version_ | 1866914184228241408 |
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| author | Amini, Hamed Amini, Nina H. Chalal, Sofiane Guo, Gaoyue |
| author_facet | Amini, Hamed Amini, Nina H. Chalal, Sofiane Guo, Gaoyue |
| contents | We study a family of essentially pairwise independent Brownian motions indexed by a continuum of labels and show how the Fubini extension framework provides a rigorous way to represent such families as a single jointly measurable process. Within this framework, we address two main objectives: first, we show how a system of graphon stochastic differential equations can be reformulated as a single McKean-Vlasov type equation driven by a standard Brownian motion, which significantly facilitates its analysis. Second, we establish a Girsanov theorem for a continuum of essentially pairwise independent Brownian motions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_12096 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Brownian motion on the Fubini extension space and applications Amini, Hamed Amini, Nina H. Chalal, Sofiane Guo, Gaoyue Probability 60J65, 28A35, 60H05 We study a family of essentially pairwise independent Brownian motions indexed by a continuum of labels and show how the Fubini extension framework provides a rigorous way to represent such families as a single jointly measurable process. Within this framework, we address two main objectives: first, we show how a system of graphon stochastic differential equations can be reformulated as a single McKean-Vlasov type equation driven by a standard Brownian motion, which significantly facilitates its analysis. Second, we establish a Girsanov theorem for a continuum of essentially pairwise independent Brownian motions. |
| title | Brownian motion on the Fubini extension space and applications |
| topic | Probability 60J65, 28A35, 60H05 |
| url | https://arxiv.org/abs/2509.12096 |