Probability of noise and rate-induced tipping

Paul Ritchie, Jan Sieber

Published 2016-06-27Version 1

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.