# Retrieving information from subordination

Abstract : We show that if $(X_s, s\geq 0)$ is a right-continuous process, $Y_t=\int_0^t\d s X_s$ its integral process and $\tau = (\tau_{\ell}, \ell \geq 0)$ a subordinator, then the time-changed process $(Y_{\tau_{\ell}}, \ell\geq 0)$ allows to retrieve the information about $(X_{\tau_{\ell}}, \ell\geq 0)$ when $\tau$ is stable, but not when $\tau$ 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.
Keywords :
Document type :
Preprints, Working Papers, ...
2010
Domain :

https://hal.archives-ouvertes.fr/hal-00484054
Contributor : Jean Bertoin <>
Submitted on : Monday, May 17, 2010 - 5:08:39 PM
Last modification on : Wednesday, October 12, 2016 - 1:04:17 AM
Document(s) archivé(s) le : Thursday, September 16, 2010 - 2:26:59 PM

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Retrieving.pdf
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### Identifiers

• HAL Id : hal-00484054, version 1
• ARXIV : 1005.3187

### Citation

Jean Bertoin, Marc Yor. Retrieving information from subordination. 2010. <hal-00484054>

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