Invariance principles for clocks

TL;DR

This paper establishes an invariance principle for rescaled clocks in positive semi-stable Markov processes, confirming a conjecture from prior research and advancing understanding of their asymptotic behavior.

Contribution

It proves a conjecture regarding the invariance principle for rescaled clocks in positive semi-stable Markov processes, filling a gap in the theoretical understanding.

Findings

Proves an invariance principle for rescaled clocks

Confirms a conjecture from Demni, Rouault, Zani (2015)

Advances theoretical understanding of semi-stable Markov processes

Abstract

We show an invariance principle for rescaled clocks of positive semi-stable Markov processes, proving a conjecture presented in Remark 4 in Demni, Rouault, Zani [11], 2015.