{
  "id": "1708.02186",
  "version": "v1",
  "published": "2017-08-07T16:18:03.000Z",
  "updated": "2017-08-07T16:18:03.000Z",
  "title": "On the strong Markov property for stochastic differential equations driven by $G$-Brownian motion",
  "authors": [
    "Mingshang Hu",
    "Xiaojun Ji",
    "Guomin Liu"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we study the stochastic differential equations driven by $G$-Brownian motion ($G$-SDEs for short). We extend the notion of conditional $G$-expectation from deterministic time to the more general optional time situation. Then, via this conditional expectation, we develop the strong Markov property for $G$-SDEs. In particular, we obtain the strong Markov property for $G$-Brownian motion. Some applications including the reflection principle for $G$-Brownian motion are also provided.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-07T16:18:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic differential equations driven",
      "strong markov property",
      "brownian motion",
      "general optional time situation",
      "deterministic time"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}