{
  "id": "2212.04766",
  "version": "v1",
  "published": "2022-12-09T10:44:03.000Z",
  "updated": "2022-12-09T10:44:03.000Z",
  "title": "Wasserstein distance estimates for jump-diffusion processes",
  "authors": [
    "Jean-Christophe Breton",
    "Nicolas Privault"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We derive Wasserstein distance bounds between the probability distributions of a stochastic integral (It\\^o) process with jumps $(X_t)_{t\\in [0,T]}$ and a jump-diffusion process $(X^\\ast_t)_{t\\in [0,T]}$. Our bounds are expressed using the stochastic characteristics of $(X_t)_{t\\in [0,T]}$ and the jump-diffusion coefficients of $(X^\\ast_t)_{t\\in [0,T]}$ evaluated in $X_t$, and apply in particular to the case of different jump characteristics. Our approach uses stochastic calculus arguments and $L^p$ integrability results for the flow of stochastic differential equations with jumps, without relying on the Stein equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-09T10:44:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H05",
      "60H10",
      "60G57",
      "60G44",
      "60J60",
      "60J76"
    ],
    "keywords": [
      "wasserstein distance estimates",
      "jump-diffusion process",
      "stochastic calculus arguments",
      "stochastic differential equations",
      "derive wasserstein distance bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}