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 analyze some basic issues associated with Generalized Poisson-Kac (GPK)stochastic processes, starting from the extended notion of the Markoviancondition. The extended Markovian nature of GPK processes is established, andthe implications of this property derived: the associated adjoint formalism forGPK processes is developed essentially in an analogous way as for theFokker-Planck operator associated with Langevin equations driven by Wienerprocesses. Subsequently, the regularity of trajectories is addressed: theoccurrence of fractality in the realizations of GPK is a long-term emergentproperty, and its implication in thermodynamics is discussed. The concept ofcompleteness in the stochastic description of GPK is also introduced. Finally,some observations on the role of correlation properties of noise sources andtheir influence on the dynamic properties of transport phenomena are addressed,using a Wiener model for comparison.

Markovian nature, completeness, regularity and correlation properties of Generalized Poisson-Kac processes