{
  "id": "2007.02174",
  "version": "v1",
  "published": "2020-07-04T19:52:47.000Z",
  "updated": "2020-07-04T19:52:47.000Z",
  "title": "1--Meixner random vectors",
  "authors": [
    "Aurel I. Stan",
    "Florin Catrina"
  ],
  "comment": "45 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "A definition of $d$--dimensional $n$--Meixner random vectors is given first. This definition involves the commutators of their semi--quantum operators. After that we will focus on the $1$-Meixner random vectors, and derive a system of $d$ partial differential equations satisfied by their Laplace transform. We provide a set of necessary conditions for this system to be integrable. We use these conditions to give a complete characterization of all non--degenerate three--dimensional $1$--Meixner random vectors. It must be mentioned that the three--dimensional case produces the first example in which the components of a $1$--Meixner random vector cannot be reduced, via an injective linear transformation, to three independent classic Meixner random variables.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-04T19:52:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C05",
      "46L53"
    ],
    "keywords": [
      "meixner random vector",
      "independent classic meixner random variables",
      "three-dimensional case produces",
      "partial differential equations",
      "laplace transform"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}