In this paper, we study intensity of jumps in the context of functional linear processes. The natural space for that is the space D = D[0, 1] of cadlag real functions. We begin with limit theorems for ARMAD(1,1) processes. It appears that under some conditions, the functional linear process and its innovation have the same jumps. This nice property allows us to focus on the case of i.i.d. D-valued random variables. For such variables, we estimate the intensity of jumps in various situations : fixed number of jumps, random instants of jumps, random number of instants of jumps, .... We derive exponential rates and limits in distribution.