{
  "id": "1606.08180",
  "version": "v1",
  "published": "2016-06-27T09:57:33.000Z",
  "updated": "2016-06-27T09:57:33.000Z",
  "title": "Probability of noise and rate-induced tipping",
  "authors": [
    "Paul Ritchie",
    "Jan Sieber"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We propose a formula to approximate the probability of rate-induced tipping with additive white noise occurring for small to moderate equilibrium drift speeds. Early-warning indicators have generally been used on historical tipping events as a form of verification. This can lead to false-positives (false alarms) and false-negatives (missed alarms) if we wish to use early-warning indicators to offer forewarning of future tipping events. Thus, quantifying the probability of tipping will give a better understanding on the measures needed to be taken. We verify the approximation on a prototypical model for rate-induced tipping with additive noise using Monte-Carlo simulations. The formula relies on slow to moderate drift but can be extended to close encounters of rate-induced tipping and otherwise is generic to all forms of tipping.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-27T09:57:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rate-induced tipping",
      "probability",
      "moderate equilibrium drift speeds",
      "early-warning indicators",
      "tipping events"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}