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/

Zendy Plus

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

Zendy Tools

Zendy Open

A stochastic approximation technique is developed so that an Rd-valued random process X in discrete or continuous time can be viewed as a limit of "simple" quantities (ξ(n)) (n≥0), subsequently called "skeletons". The important feature of the approximation is that convergence is understood in the strongest possible sense, not only for the processes (where pathwise convergence is required), but also for the underlying filtrations (for which a natural convergence concept is introduced): the simple processes ξ(n) take finitely many different values at any point in time, change values at a finite number of times and possess an information structure (filtration) that is discrete and finite. The constructions provide a tool to explicitly deal with the fine structure of a given filtration and can be used to gain insight into the dynamic nature of the underlying process. The sequences of skeletons that are constructed (i) approximate a given random process X pathwise and (ii) preserve structural properties of X (for example, (sub-, super-) martingale property, martingale representation property, Markov property) by means of convergence of information. This ability to "deal with information" is illustrated with a variety of examples, including pathwise approximations of standard Brownian motion in one and higher dimensions.

Pathwise approximations of processes based on the fine structure of their filtrations