{
  "id": "1612.06125",
  "version": "v1",
  "published": "2016-12-19T11:18:40.000Z",
  "updated": "2016-12-19T11:18:40.000Z",
  "title": "Sticky couplings of multidimensional diffusions with different drifts",
  "authors": [
    "Andreas Eberle",
    "Raphael Zimmer"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We present a novel approach of coupling two multidimensional and non-degenerate It\\^o processes $(X_t)$ and $(Y_t)$ which follow dynamics with different drifts. Our coupling is sticky in the sense that there is a stochastic process $(r_t)$, which solves a one-dimensional stochastic differential equation with a sticky boundary behavior at zero, such that almost surely $|X_t-Y_t|\\leq r_t$ for all $t\\geq 0$. The coupling is constructed as a weak limit of Markovian couplings. We provide explicit, non-asymptotic and long-time stable bounds for the probability of the event $\\{X_t=Y_t\\}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-19T11:18:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J60",
      "60H10"
    ],
    "keywords": [
      "multidimensional diffusions",
      "sticky couplings",
      "one-dimensional stochastic differential equation",
      "sticky boundary behavior",
      "stochastic process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}