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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Prediction via deterministic continuous-time models will always be subject tomodel error, for example due to unexplainable phenomena, uncertainties in anydata driving the model, or discretisation/resolution issues. In this paper, webuild upon previous small-noise studies to provide an explicit bound for theerror between a general class of stochastic differential equations andcorresponding computable linearisations written in terms of a deterministicsystem. Our framework accounts for non-autonomous coefficients, multiplicativenoise, and uncertain initial conditions. We demonstrate the predictive power ofour bound on diverse numerical case studies. We confirm that our bound issharp, in that it accurately predicts the error scaling in the moments of thelinearised approximation as both the uncertainty in the initial condition andthe magnitude of the noise in the differential equation are altered. This paperalso provides an extension of stochastic sensitivity, a recently introducedtool for quantifying uncertainty in dynamical systems, to arbitrary dimensionsand establishes the link to our characterisation of stochastic differentialequation linearisations.

The convergence of stochastic differential equations to their linearisation in small noise limits