{
  "id": "1903.12325",
  "version": "v1",
  "published": "2019-03-29T02:22:48.000Z",
  "updated": "2019-03-29T02:22:48.000Z",
  "title": "Entropy flow and De Bruijn's identity for a class of stochastic differential equations driven by fractional Brownian motion",
  "authors": [
    "Michael C. H. Choi",
    "Chihoon Lee",
    "Jian Song"
  ],
  "comment": "10 pages",
  "categories": [
    "math.PR",
    "cs.IT",
    "math.IT"
  ],
  "abstract": "Motivated by the classical De Bruijn's identity for the additive Gaussian noise channel, in this paper we consider a generalized setting where the channel is modelled via stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H\\in(1/4,1)$. We derive generalized De Bruijn's identity for Shannon entropy and Kullback-Leibler divergence by means of It\\^o's formula, and present two applications where we relax the assumption to $H \\in (0,1)$. In the first application we demonstrate its equivalence with Stein's identity for Gaussian distributions, while in the second application, we show that for $H \\in (0,1/2]$, the entropy power is concave in time while for $H \\in (1/2,1)$ it is convex in time when the initial distribution is Gaussian. Compared with the classical case of $H = 1/2$, the time parameter plays an interesting and significant role in the analysis of these quantities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-29T02:22:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G22",
      "60G15"
    ],
    "keywords": [
      "stochastic differential equations driven",
      "fractional brownian motion",
      "bruijns identity",
      "entropy flow",
      "gaussian noise channel"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}