{
  "id": "1908.01641",
  "version": "v1",
  "published": "2019-08-05T14:19:25.000Z",
  "updated": "2019-08-05T14:19:25.000Z",
  "title": "Average preserving variation processes in view of optimization",
  "authors": [
    "Lassalle",
    "Rémi"
  ],
  "comment": "This is a working paper",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, within the specific framework of an intrinsic calculus of variations on laws of semi-martingales, which is based on information flows preserving perturbations, we investigate least action principles associated to average preserving variation processes. The associated Euler-Lagrange conditions, which we obtain, exhibit a deterministic process aside the canonical martingale term. In particular, taking specific action functionals, we have that critical processes with respect to those variations encompass specific laws of continuous semi-martingales whose drift characteristic is integrable with independent increments. Then, we relate critical processes of classical cost functions to a specific class of forward-backward systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-05T14:19:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "average preserving variation processes",
      "optimization",
      "variations encompass specific laws",
      "critical processes",
      "deterministic process aside"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}