Local time analysis of additive Lévy processes with different Lévy exponents

Let X1, …, XN be independent, classical Lévy processes on ℝd with Lévy exponents Ψ1, …, ΨN, respectively. The corresponding additive Lévy process is defined as the following N-parameter random field on ℝd, X(t) ≜ X1(t1)+ … + XN (tN), ∀t ∈ ℝN+. Under mild regularity conditions on the Ψi's, we derive estimate for the local and uniform moduli of continuity of local times of X = {X(t); t ∈ ℝN+}.