In contrast to conventional airborne multi-echo laser scanner systems, full-waveform (FW) lidar systems are able to record the entire emitted and backscattered signals of each laser pulse. Instead of clouds of individual 3D points, FW devices provide 1D profiles of the 3D scene, which allows gaining additional and more detailed observations of the illuminated surfaces. Indeed, lidar waveforms are signals consisting of a train of echoes where each of them corresponds to a scattering target of the Earth surface or a group of close objects leading to superimposed signals. Modelling these echoes with the appropriate parametric function is necessary to retrieve physical information about these objects and characterize their properties. Henceforth, the extracted parameters can be useful for subsequent object segmentation and/or classification. This paper presents a stochastic based model to reconstruct lidar waveforms in terms of a set of parametric functions. The model takes into account both a data term which measures the coherence between the proposed configurations and the waveforms, and a regularizing term which introduces physical knowledge on the reconstructed signal. We search for the best configuration of functions by performing a Reversible Jump Markov Chain Monte Carlo sampler coupled with a stochastic relaxation. Finally, the algorithm is validated on waveforms from several airborne lidar sensors, showing the suitability of the approach even when the traditional assumption of Gaussian decomposition of waveforms is invalid.