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 consider a diffusion process under a local weak H\"{o}rmander condition onthe coefficients. We find Gaussian estimates for the density in short time andexponential lower and upper bounds for the probability that the diffusionremains in a small tube around a deterministic trajectory (skeleton path),explicitly depending on the radius of the tube and on the energy of theskeleton path. We use a norm which reflects the non-isotropic structure of theproblem, meaning that the diffusion propagates in $\mathbb{R}^2$ with differentspeeds in the directions $\sigma$ and $[\sigma,b]$. We establish a connectionbetween this norm and the standard control distance.

Tube estimates for diffusion processes under a weak H\"ormander condition