Retrieving information from subordination
Jean Bertoin (PMA, DMA), Marc Yor (PMA, IUF)

TL;DR
The paper investigates how time-changing processes with subordinators affects the retrieval of original process information, highlighting differences between stable and gamma subordinators, motivated by identities involving Bessel clocks and inverse Gaussian variables.
Contribution
It demonstrates that stable subordinators enable retrieval of original process information after time change, unlike gamma subordinators, revealing a key distinction in stochastic process transformations.
Findings
Stable subordinators preserve information about the original process.
Gamma subordinators do not allow such information retrieval.
The results are motivated by identities involving Bessel clocks and inverse Gaussian variables.
Abstract
We show that if is a right-continuous process, its integral process and a subordinator, then the time-changed process allows to retrieve the information about when is stable, but not when is a gamma subordinator. This question has been motivated by a striking identity in law involving the Bessel clock taken at an independent inverse Gaussian variable.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
