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

B-series and generalizations are a powerful tool for the analysis ofnumerical integrators. An extension named exotic aromatic B-series wasintroduced to study the order conditions for sampling the invariant measure ofergodic SDEs. Introducing a new symmetry normalization coefficient, we analyzethe algebraic structures related to exotic B-series and S-series. Precisely, weprove the relationship between the Grossman-Larson algebras over exotic andgrafted forests and the corresponding duals to the Connes-Kreimer coalgebrasand use it to study the natural composition laws on exotic S-series. Applyingthis algebraic framework to the derivation of order conditions for a class ofstochastic Runge-Kutta methods, we present a multiplicative property thatensures some order conditions to be satisfied automatically.

Exotic B-series and S-series: algebraic structures and order conditions for invariant measure sampling