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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We explore the properties of discrete-time stochastic processes with abounded state space, whose deterministic limit is given by a map of the unitinterval. We find that, in the mesoscopic description of the system, the largejumps between successive iterates of the process can result in probabilityleaking out of the unit interval, despite the fact that the noise ismultiplicative and vanishes at the boundaries. By including higher-order termsin the mesoscopic expansion, we are able to capture the non-Gaussian nature ofthe noise distribution near the boundaries, but this does not preclude thepossibility of a trajectory leaving the interval. We propose a number ofprescriptions for treating these escape events, and we compare the results withthose obtained for the metastable behavior of the microscopic model, whereescape events are not possible. We find that, rather than truncating the noisedistribution, censoring this distribution to prevent escape events leads toresults which are more consistent with the microscopic model. The addition ofhigher moments to the noise distribution does not increase the accuracy of thefinal results, and it can be replaced by the simpler Gaussian noise.

Suppressing escape events in maps of the unit interval with demographic noise