1 INTRODUCTION State space models are important tools in many scientific and engineering disciplines, including control theory, statistics and computational neuroscience. In this article, we study the time-invariant ℝ k -valued state space model ( 𝒜 , ℬ , 𝒞 , L ) of dimension k p , that is characterised by a driving ℝ k -valued Lévy process L = ( L ( t ) ) t ∈ ℝ , a state transition matrix 𝒜 ∈ ℝ k p × k p with p ∈ ℕ , an input matrix ℬ ∈ ℝ k p × k , and an observation matrix 𝒞 ∈ ℝ k p × k .
