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.

Bertoin, J; Yor, M (2013). *Retrieving information from subordination.* Springer Proceedings in Mathematics & Statistics, 133:97-106.

## 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.

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## Additional indexing

Item Type: | Journal Article, refereed, original work |
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Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |

Dewey Decimal Classification: | 510 Mathematics |

Language: | English |

Date: | 2013 |

Deposited On: | 17 Apr 2013 08:50 |

Last Modified: | 05 Apr 2016 16:44 |

Publisher: | Springer |

ISSN: | 2194-1009 |

Additional Information: | ISBN: 978-3-642-33548-8 |

Publisher DOI: | https://doi.org/10.1007/978-3-642-33549-5_5 |

Related URLs: | http://arxiv.org/abs/1005.3187 |

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