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 extend the It\^o-Wentzell formula for the evolution along a continuoussemimartingale of a time-dependent stochastic field driven by a continuoussemimartingale to tensor field-valued stochastic processes on manifolds. Moreconcretely, we investigate how the pull-back (respectively, the push-forward)by a stochastic flow of diffeomorphisms of a time-dependent stochastic tensorfield driven by a continuous semimartingale evolves with time, deriving itunder suitable regularity conditions. We call this result theKunita-It\^o-Wentzell (KIW) formula for the advection of tensor-valuedstochastic processes. Equations of this nature bear significance in stochasticfluid dynamics and well-posedness by noise problems, facilitating thedevelopment of certain geometric extensions within existing theories.

A Geometric Extension of the It\^o-Wentzell and Kunita's Formulas