Anomalous jumping in a double-well potential

Abstract

Noise induced jumping between meta-stable states in a potential depends on the structure of the noise. For an $\alpha$-stable noise, jumping triggered by single extreme events contributes to the transition probability. This is also called Levy flights and might be of importance in triggering sudden changes in geophysical flow and perhaps even climatic changes. The steady state statistics is also influenced by the noise structure leading to a non-Gibbs distribution for an $\alpha$-stable noise.