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

L\'evy-type perpetuities being the a.s. limits of particular generalizedOrnstein-Uhlenbeck processes are a natural continuous-time generalization ofdiscrete-time perpetuities. These are random variables of the form$S:=\int_{[0,\infty)}e^{-X_{s-}}{\mathrm{d}}Z_s$, where $(X,Z)$ is atwo-dimensional L\'evy process, and $Z$ is a drift-free L\'evy process ofbounded variation. We prove an ultimate criterion for the finiteness of powermoments of $S$. This result and the previously known assertion due to Ericksonand Maller (2005) concerning the a.s. finiteness of $S$ are then used to deriveultimate necessary and sufficient conditions for the $L_p$-convergence for$p>1$ and $p=1$, respectively, of Biggins' martingales associated to branchingL\'evy processes. In particular, we provide final versions of results obtainedrecently by Bertoin and Mallein (2018).

alea

A result on power moments of L\'evy-type perpetuities and its  application to the $L_p$-convergence of Biggins' martingales in branching  L\'evy processes