On approximations of the point measures associated with the Brownian web by means of the fractional step method and the discretization of the initial interval
UDC 519.21 We establish the rate of weak convergence in the fractional step method for the Arratia flow in terms of the Wasserstein distance between the images of the Lebesque measure under the action of the flow. We introduce finite-dimensional densities that describe sequences of collisions in the...
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| Date: | 2020 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2020
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/6279 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 519.21
We establish the rate of weak convergence in the fractional step method for the Arratia flow in terms of the Wasserstein distance between the images of the Lebesque measure under the action of the flow. We introduce finite-dimensional densities that describe sequences of collisions in the Arratia flow and derive an explicit expression for them. With the initial interval discretized, we also discuss the convergence of the corresponding approximations of the point measure associated with the Arratia flow in terms of such densities. |
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| DOI: | 10.37863/umzh.v72i9.6279 |