{
  "id": "2303.10245",
  "version": "v1",
  "published": "2023-03-17T20:50:02.000Z",
  "updated": "2023-03-17T20:50:02.000Z",
  "title": "Martingale-driven integrals and singular SPDEs",
  "authors": [
    "Paolo Grazieschi",
    "Konstantin Matetski",
    "Hendrik Weber"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-17T20:50:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "singular spdes",
      "martingale-driven integrals",
      "multiple wiener stochastic integrals",
      "three-dimensional ising-kac model",
      "singular stochastic pdes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}