English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We introduce a new method, allowing to describe slowly time-dependentLangevin equations through the behaviour of individual paths. This approachyields considerably more information than the computation of the probabilitydensity. The main idea is to show that for sufficiently small noise intensityand slow time dependence, the vast majority of paths remain in small space-timesets, typically in the neighbourhood of potential wells. The size of these setsoften has a power-law dependence on the small parameters, with universalexponents. The overall probability of exceptional paths is exponentially small,with an exponent also showing power-law behaviour. The results cover time spansup to the maximal Kramers time of the system. We apply our method to threephenomena characteristic for bistable systems: stochastic resonance, dynamicalhysteresis and bifurcation delay, where it yields precise bounds on transitionprobabilities, and the distribution of hysteresis areas and first-exit times.We also discuss the effect of coloured noise.Comment: 37 pages, 11 figure

Beyond the Fokker-Planck equation: pathwise control of noisy bistable systems