Estimation non-param\'etrique de la densit\'e spectrale d'un processus   gaussien \'echantillonn\'e al\'eatoirement
  From a wavelet analysis, one derives a nonparametrical estimator for the spectral density of a Gaussian process with stationary increments. First, the idealistic case of a continuous time path of the process is considered. A punctual Central Limit Theorem (CLT) and an estimation of the Mean Integrate Square Error (MISE) are established. Next, to fit the applications, one considers the case where one observes a path at random times. One built a second estimator obtained by replacing the wavelet coefficients by their discretizations. A second CLT and the corresponding estimation of the MISE are provided. Finally, simulation results and an application on the heartbeat time series of marathon runners are presented. 
Jean-Marc Bardet (CES, SAMOS), Pierre Bertrand (LMA-Clermont),   V\'eronique Billat (LEPHE)