| Autor: |
Grazieschi, Paolo, Matetski, Konstantin, Weber, Hendrik |
| Rok vydání: |
2023 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
We consider multiple stochastic integrals with respect to c\`adl\`ag martingales, which approximate a cylindrical Wiener process. We define a chaos expansion, analogous to the case of multiple Wiener stochastic integrals, for these integrals and use it to show moment bounds. Key tools include an iteration of the Burkholder-Davis-Gundy inequality and a multi-scale decomposition similar to the one developed in arXiv:1512.07845. Our method can be combined with the recently developed discretisation framework for regularity structures arXiv:1511.06937, arXiv:1705.02836 to prove convergence of interacting particle systems to singular stochastic PDEs. A companion article titled "The dynamical Ising-Kac model in 3D converges to $\Phi^4_3$" applies the results of this paper to prove convergence of a rescaled Glauber dynamics for the three-dimensional Ising-Kac model near criticality to the $\Phi^4_3$ dynamics on a torus. |
| Databáze: |
arXiv |
| Externí odkaz: |
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