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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We develop a probabilistic characterisation of trajectorial expansion ratesin non-autonomous stochastic dynamical systems that can be defined over afinite time interval and used for the subsequent uncertainty quantification inLagrangian (trajectory-based) predictions. These expansion rates are quantifiedvia certain divergences (pre-metrics) between probability measures induced bythe laws of the stochastic flow associated with the underlying dynamics. Weconstruct scalar fields of finite-time divergence/expansion rates, show theirexistence and space-time continuity for general stochastic flows. Combiningthese divergence rate fields with our 'information inequalities' derived inallows for quantification and mitigation of the uncertainty in path-basedobservables estimated from simplified models in a way that is amenable toalgorithmic implementations, and it can be utilised in information-geometricanalysis of statistical estimation and inference, as well as in a data-drivenmachine/deep learning of coarse-grained models. We also derive a link betweenthe divergence rates and finite-time Lyapunov exponents for probabilitymeasures and for path-based observables.

Measures of path-based nonlinear expansion rates and Lagrangian uncertainty in stochastic flows