“…In the statement below [∞] will refer to N. There exists a polynomial basis {f i , i ∈ N} (depending on d) such that for any K ∈ N ∪ {∞}, the process (tr f k (G(s + t)), k ∈ [K], t ≥ 0) converges in law, as s tends to infinity, to the Markov process (N k (t), k ∈ [K], t ≥ 0) of Theorem 1. [The polynomials are given explicitly in (16).] Hence, for any polynomial f , the process (tr f (G(s + t))) converges to a linear combination of the coordinate processes of (N k (t), k ∈ N).…”