{
  "id": "2403.16000",
  "version": "v1",
  "published": "2024-03-24T04:04:05.000Z",
  "updated": "2024-03-24T04:04:05.000Z",
  "title": "Stochastic maximum principle for weighted mean-field system with jump",
  "authors": [
    "Yanyan Tang",
    "Jie Xiong"
  ],
  "categories": [
    "math.OC",
    "math.PR"
  ],
  "abstract": "In this article, we consider a weighted mean-field control problem with jump-diffusion as its state process. The main difficulty is from the non-Lipschitz property of the coefficients. We overcome this difficulty by an $L_{p,q}$-estimate of the solution processes with a suitably chosen $p$ and $q$. Convex pertubation method combining with the aforementioned $L_{p,q}$-estimation method is utilized to derive the stochastic maximum principle for this control problem. A sufficient condition for the optimality is also given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-24T04:04:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic maximum principle",
      "weighted mean-field system",
      "weighted mean-field control problem",
      "convex pertubation method",
      "sufficient condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}