A Theoretical results

This section contains details on our theoretical results. A.3 Proof of Proposition 1 For the convenience of reading, we defer the derivation details of all equations to Appendix A.2. This implies that the right inequality represents not only the necessary but also (approximately) the sufficient condition for a δ -jump when δ is small. A.4 On β -undetermined recurrent sequences Here we provide some results related to convergence of sequences of the following kind: x We will prove the first statement since the second one can be proved similarly. Now, if it holds, we can apply Proposition 5 and conclude the proof.