{
  "id": "0711.1887",
  "version": "v1",
  "published": "2007-11-12T22:55:50.000Z",
  "updated": "2007-11-12T22:55:50.000Z",
  "title": "A Class of Infinite Dimensional Diffusion Processes with Connection to Population Genetics",
  "authors": [
    "Shui Feng",
    "Feng-Yu Wang"
  ],
  "comment": "14 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Starting from a sequence of independent Wright-Fisher diffusion processes on $[0,1]$, we construct a class of reversible infinite dimensional diffusion processes on $\\DD_\\infty:= \\{{\\bf x}\\in [0,1]^\\N: \\sum_{i\\ge 1} x_i=1\\}$ with GEM distribution as the reversible measure. Log-Sobolev inequalities are established for these diffusions, which lead to the exponential convergence to the corresponding reversible measures in the entropy. Extensions are made to a class of measure-valued processes over an abstract space $S$. This provides a reasonable alternative to the Fleming-Viot process which does not satisfy the log-Sobolev inequality when $S$ is infinite as observed by W. Stannat \\cite{S}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-11-12T22:55:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F10",
      "92D10"
    ],
    "keywords": [
      "population genetics",
      "log-sobolev inequality",
      "reversible infinite dimensional diffusion processes",
      "independent wright-fisher diffusion processes",
      "connection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.1887F"
    }
  }
}