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

We investigate the stationary measure $\pi$ of SDEs driven by additivefractional noise with any Hurst parameter and establish that $\pi$ admits asmooth Lebesgue density obeying both Gaussian-type lower and upper bounds. Theproofs are based on a novel representation of the stationary density in termsof a Wiener-Liouville bridge, which proves to be of independent interest: Weshow that it also allows to obtain Gaussian bounds on the non-stationarydensity, which extend previously known results in the additive setting. Inaddition, we study a parameter-dependent version of the SDE and provesmoothness of the stationary density, jointly in the parameter and the spatialcoordinate. With this we revisit the fractional averaging principle of Li andSieber [Ann. Appl. Probab. 32(5) (2022)] and remove an ad-hoc assumption on thelimiting coefficients. Avoiding any use of Malliavin calculus in our arguments,we can prove our results under minimal regularity requirements.

On the (Non-)Stationary Density of Fractional-Driven Stochastic Differential Equations