In the thesis, a recently proposed urn-based model with triggering, describing how novelties and innovations emerge in real systems, is studied. Through the urn process a sequence is generated. Relevant statistics can be studied such as how many distinct elements appear in the sequence until a certain time and the frequency with which each of the elements has been observed. These two statistics turn out to follow the Heaps' and Zipf's law, respectively and some heuristic arguments have been proposed in the literature to justify the emergence of these laws. One of the main contributions of this thesis consists in providing rigorous proofs for these results.