We offer a new methodology for the assessment of public debt sustainability in a stochastic economy when sovereign default taken into account. The default threshold differs from the no-Ponzi condition and depends on the post-default debt recovery rule. We distinguish sustainability and unsustainability conditions, related to alternative scenarios on the future sequence of shocks. We highlight the role of the debt recovery ratio on the whole dynamics of public debt. When a sovereign default occurs, the sustainability of the post-default debt is ensured when the haircut is sufficiently large. Lastly we provide an explanation of serial defaults.