The Coding Complexity of Lévy Processes

In this article, we study the coding problem for real-valued Lévy processes X (original) under Lp[0, 1]-norm distortion for some fixed p ∈ [1,∞). Here we think of X being a D[0,∞)-valued process, where D[0,∞) denotes the space of càdlàg functions endowed with the Skorohod topology. We shall denote by ‖ · ‖ the standard Lp[0, 1]-norm. Let 0 < s ≤ ∞. The objective is now to find a càdlàg real-valued process X̂ (reconstruction or approximation) that minimizes the error criterion