{
  "id": "1509.01783",
  "version": "v1",
  "published": "2015-09-06T08:00:01.000Z",
  "updated": "2015-09-06T08:00:01.000Z",
  "title": "Lyapunov Functions for Reflected Jump-Diffusions",
  "authors": [
    "Andrey Sarantsev"
  ],
  "comment": "26 pages. Keywords: Jump-diffusion processes, reflected diffusions, oblique reflection, positive orthant, reflected jump-diffusions, Lyapunov function, uniform ergodicity, tail estimate, stationary distribution, stochastic ordering, jump measures, competing Levy particles, gap process. arXiv admin note: text overlap with arXiv:1509.01781",
  "categories": [
    "math.PR"
  ],
  "abstract": "For a multidimensional jump-diffusion process, we construct a Lyapunov function and prove its exponential ergodicity. We do the same for obliquely reflected jump-diffusion processes in the positive orthant, extending results of Atar, Budhiraja and Dupuis (2001). We apply these results to systems of competing L\\'evy particles, introduced in Shkolnikov (2011).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-06T08:00:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J60",
      "60J55",
      "60J75",
      "60G51",
      "60J65",
      "60H10",
      "60K35"
    ],
    "keywords": [
      "lyapunov function",
      "multidimensional jump-diffusion process",
      "exponential ergodicity",
      "obliquely reflected jump-diffusion processes",
      "competing levy particles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}