A criterion for right continuity of filtrations generated by group-valued additive processes

Let X={X(t),t[set membership, variant]T} be a stochastic process with independent increments indexed by the multidimensional set of parameters T=(R+)q, q[greater-or-equal, slanted]1, taking values in a T0 topological Abelian group G. In this note, we give conditions under which the filtration , t[set membership, variant]T, generated by the process X is right continuous, i.e. for all t[set membership, variant]T.