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

This paper is concerned with stochastic systems whose state is a diffusionprocess governed by an Ito stochastic differential equation (SDE). In theframework of a nominal white-noise model, the SDE is driven by a standardWiener process. For a scenario of statistical uncertainty, where the drivingnoise acquires a state-dependent drift and thus deviates from its idealisedmodel, we consider the perturbation of the invariant probability densityfunction (PDF) as a steady-state solution of the Fokker-Planck-Kolmogorovequation. We discuss an upper bound on a logarithmic Dirichlet form for theratio of the invariant PDF to its nominal counterpart in terms of theKullback-Leibler relative entropy rate of the actual noise distribution withrespect the Wiener measure. This bound is shown to be achievable, provided thePDF ratio is preserved by the nominal steady-state probability flux. Thelogarithmic Dirichlet form bound is used in order to obtain an upper bound onthe relative entropy of the perturbed invariant PDF in terms ofquadratic-exponential moments of the noise drift in the uniform ellipticitycase. These results are illustrated for perturbations of Gaussian invariantmeasures in linear stochastic systems involving linear noise drifts.

Entropy bounds for invariant measure perturbations in stochastic systems with uncertain noise