{
  "id": "1905.04843",
  "version": "v1",
  "published": "2019-05-13T03:03:08.000Z",
  "updated": "2019-05-13T03:03:08.000Z",
  "title": "Periodic solutions of stochastic differential equations driven by Lévy noises",
  "authors": [
    "Xiao-Xia Guo",
    "Wei Sun"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we first show the well-posedness of the SDEs driven by L\\'{e}vy noises under mild conditions. Then, we consider the existence and uniqueness of periodic solutions of the SDEs. To establish the ergodicity and uniqueness of periodic solutions, we investigate the strong Feller property and the irreducibility of the corresponding time-inhomogeneous semigroups when both small and large jumps are allowed in the equations. Some examples are presented to illustrate our results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-13T03:03:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "60J75",
      "34C25",
      "37B25"
    ],
    "keywords": [
      "stochastic differential equations driven",
      "periodic solutions",
      "lévy noises",
      "strong feller property",
      "mild conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}