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 show that a one-dimensional regular continuous Markov process \(\X\) withscale function \(s\) is a Feller--Dynkin process precisely if the spacetransformed process \(s (X)\) is a martingale when stopped at the boundaries ofits state space. As a consequence, the Feller--Dynkin and the martingaleproperty are equivalent for regular diffusions on natural scale with open statespace. By means of a counterexample, we also show that this equivalence failsfor multi-dimensional diffusions. Moreover, for It\^o diffusions we discussrelations to Cauchy problems.

On the Feller-Dynkin and the Martingale Property of One-Dimensional Diffusions