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 class $\mathscr{X}$ of continuous functions on $[0,1]$ that isof interest from two different perspectives. First, it is closely related tosets of functions that have been studied as generalizations of the Takagifunction. Second, each function in $\mathscr{X}$ admits a linear pathwisequadratic variation and can thus serve as an integrator in F\"ollmer's pathwiseIt\=o calculus. We derive several uniform properties of the class$\mathscr{X}$. For instance, we compute the overall pointwise maximum, theuniform maximal oscillation, and the exact uniform modulus of continuity forall functions in $\mathscr{X}$. Furthermore, we give an example of a pair$x,y\in\mathscr{X}$ such that the quadratic variation of the sum $x+y$ does notexist.

On a class of generalized Takagi functions with linear pathwise quadratic variation