{
  "id": "2406.09678",
  "version": "v1",
  "published": "2024-06-14T03:01:33.000Z",
  "updated": "2024-06-14T03:01:33.000Z",
  "title": "Convergence rate of nonlinear delayed McKean-Vlasov SDEs driven by fractional Brownian motions",
  "authors": [
    "Shengrong Wang",
    "Jie Xie",
    "Li Tan"
  ],
  "categories": [
    "math.NA",
    "cs.NA",
    "math.PR"
  ],
  "abstract": "In this paper, our main aim is to investigate the strong convergence for a McKean-Vlasov stochastic differential equation with super-linear delay driven by fractional Brownian motion with Hurst exponent $H\\in(1/2, 1)$. After giving uniqueness and existence for the exact solution, we analyze the properties including boundedness of moment and propagation of chaos. Besides, we give the Euler-Maruyama (EM) scheme and show that the numerical solution converges strongly to the exact solution. Furthermore, a corresponding numerical example is given to illustrate the theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-14T03:01:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlinear delayed mckean-vlasov sdes driven",
      "fractional brownian motion",
      "convergence rate",
      "mckean-vlasov stochastic differential equation",
      "exact solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}