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Retrieving Information from Subordination

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 33)

Abstract

We recall some instances of the recovery problem of a signal process hidden in an observation process. Our main focus is then to show that if \((X_{s},\,s\,\geq \,0)\) is a right-continuous process, \(Y _{t} = \int \limits _{0}^{t}X_{s}\mathrm{d}s\) its integral process and \(\tau = (\tau _{u},u \geq 0)\) a subordinator, then the time-changed process \((Y _{\tau _{u}},\,u\,\geq \,0)\) allows to retrieve the information about \((X_{\tau _{v}},\,v\,\geq \,0)\) when τ is stable, but not when τ 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

Recovery problem Subordination Bougerol’s identity 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Laboratoire de Probabilités et Modèles AléatoiresUPMCParis cedex 05France
  2. 2.Institut Universitaire de France and Laboratoire de Probabilités et Modèles AléatoiresUPMCParis cedex 05France

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