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

Combining fractional calculus and the Rough Path Theory we study theexistence and uniqueness of mild solutions to evolutions equations driven by aH\"older continuous function with H\"older exponent in $(1/3,1/2)$. Ourstochastic integral is in some sense a generalization of the well-known Youngintegral and can be defined independently of the initial condition. Similar tothe Rough Path Theory we establish a second variable which is given, roughlyspeaking, by a tensor product. It is then necessary to formulate a secondequation for this new variable, and we do in a mild sense. The crucial point inorder to get this new equation is to construct a tensor depending on the noisepath but also on the semigroup. We then prove the existence of a uniqueH\"older continuous solution of the system of equations, consisting of the pathand the area components, if the nonlinear term and the initial condition aresufficiently smooth. Once the abstract theory is developed, we can present apathwise nonlinear SPDE driven by a fractional Brownian motion with Hurstparameter in $(1/3,1/2]$.

Pathwise solutions to stochastic partial differential equations driven by fractional Brownian motions with Hurst parameters in $(1/3,1/2]$