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.
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2010
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Submitted on : Monday, May 17, 2010 - 5:08:39 PM
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  • HAL Id : hal-00484054, version 1
  • ARXIV : 1005.3187

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Jean Bertoin, Marc Yor. Retrieving information from subordination. 2010. 〈hal-00484054〉

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