Regularization of trajectories for multiparameter additive processes in groups

We establish a version of the maximal inequality for multiparameter stochastic processes with independent increments taking values in T0 topological Abelian groups. As an application of this inequality, we prove the existence of a modification without discontinuities of the second kind for a multiparameter group-valued additive process. Moreover, we obtain a necessary and sufficient condition which ensures the existence of a continuous modification for such a process.