Cone-additive processes in duals of nuclear Fréchet spaces

摘要

For an additive process (Xt)t≥0 with values in the dual of a nuclear Fréchet space Φ′ = ∪∞p=0 Φ-p and for each finite time T > 0, the existence of an equivalent additive process (Xt)0≤t≤T which takes values in a Hilbert space Φ-pT is shown. The additive process takes values in a cone C′ □Φ′ if and only if it has a special Lévy-Khintchine representation and in this case for each T > 0 there exists a pathwise version (Yt)0≤t≤T in some Hilbert space Φ-qT.