{
  "id": "2007.04040",
  "version": "v1",
  "published": "2020-07-08T11:31:46.000Z",
  "updated": "2020-07-08T11:31:46.000Z",
  "title": "Some Distributional Properties of Linear Stochastic Differential Equations",
  "authors": [
    "Xue Dong He",
    "Zhaoli Jiang"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we prove a sufficient and necessary condition for the transition probability distribution of a general, time-inhomogeneous linear SDE to possess a density function and study the differentiability of the density function and the transition quantile function of the SDE. Moreover, we completely characterize the support of the marginal distribution of this SDE.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-08T11:31:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "linear stochastic differential equations",
      "distributional properties",
      "density function",
      "transition probability distribution",
      "marginal distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}