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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/2406.19810 |
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| _version_ | 1866914851028205568 |
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| author | Beiglböck, Mathias Pflügl, Susanne Schrott, Stefan |
| author_facet | Beiglböck, Mathias Pflügl, Susanne Schrott, Stefan |
| contents | Causal optimal transport and adapted Wasserstein distance have applications in different fields from optimization to mathematical finance and machine learning. The goal of this article is to provide equivalent formulations of these concepts in classic probabilistic language. In particular, we prove a Skorokhod representation theorem for adapted weak convergence, reformulate the equivalence of stochastic processes using Markovian lifts, and give an expression for the adapted Wasserstein distance based on representing processes on a common stochastic basis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19810 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Probabilistic View on the Adapted Wasserstein Distance Beiglböck, Mathias Pflügl, Susanne Schrott, Stefan Probability Causal optimal transport and adapted Wasserstein distance have applications in different fields from optimization to mathematical finance and machine learning. The goal of this article is to provide equivalent formulations of these concepts in classic probabilistic language. In particular, we prove a Skorokhod representation theorem for adapted weak convergence, reformulate the equivalence of stochastic processes using Markovian lifts, and give an expression for the adapted Wasserstein distance based on representing processes on a common stochastic basis. |
| title | A Probabilistic View on the Adapted Wasserstein Distance |
| topic | Probability |
| url | https://arxiv.org/abs/2406.19810 |