Limit Theorems for Trawl Processes

Abstract

In this work we derive limit theorems for trawl processes. First, we study the asymptotic behaviour of the partial sums of the discretized trawl process (X i∆n ) nt −1 i=0, under the assumption that as n ↑ ∞, ∆ n ↓ 0 and n∆ n → µ ∈ [0, +∞]. Second, we derive a functional limit theorem for trawl processes as the Lévy measure of the trawl seed grows to infinity and show that the limiting process has a Gaussian moving average representation.