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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

In this paper we study pseudo-processes related to odd-order heat-typeequations composed with L\'evy stable subordinators. The aim of the article istwofold. We first show that the pseudo-density of the subordinatedpseudo-process can be represented as an expectation of damped oscillations withgeneralized gamma distributed parameters. This stochastic representation alsoarises as the solution to a fractional diffusion equation, involving ahigher-order Riesz-Feller operator, which generalizes the odd-order heat-typeequation. We then prove that, if the stable subordinator has a suitableexponent, the time-changed pseudo-process becomes a genuine L\'evy stableprocess. This result permits us to obtain a power series representation for theprobability density function of an arbitrary asymmetric stable process ofexponent $\nu>1$ and skewness parameter $\beta$, with $0<\lvert\beta\lvert<1$.The methods we use in order to carry out our analysis are based on the study ofa fractional Airy function which emerges in the investigation of thehigher-order Riesz-Feller operator.

Stable distributions and pseudo-processes related to fractional Airy functions