In this master's thesis, we give a new integral characterization of Pitman-Yor processes. It is inspired by a similar characterization for Dirichlet processes given by G. Last in 2019. The proof makes use of classical point processes theory arguments and is based on a key result found by T. Lehéricy in his 2015 master's thesis. In addition, we give (Appendice C) an application of this integral equation to the computation of the moments of the random mass of a Borel set given by a Pitman-Yor process.