Detecting instants of jumps and estimating their intensity in the context of p derivatives with continuous or discrete data

In this article, we consider the ARD(p)(1) process where D[0, 1] is the space of cadlag function and the pth derivative has a possible jump. One envisages to detect the position and intensity of jump in the context of p derivatives with continuous or discrete data. We also envisage jump for the (p + 1)th derivative. The main result allows to detect jump and to detect intensity of jump simultaneously. Asymptotic results are derived.