This article discusses the problem of existence of jointly continuous self-intersection local time for an additive l´evy process. Here, ”local time” is understood in the sense of occupation density, and by an additive L´evy process the authors mean a process X = {X(t), t 2 RN+)} which has the decomposition X = X1 X2 · · ·XN, each X? has the lower index ?, = min{ 1, · · · , N}. Let Z = (Xt2 − Xt1 , · · · ,Xtr − Xtr−1 ).
They prove that if Nr > d(r − 1), then a jointly continuous local time of Z, i.e. the self-intersection local time of X, can be obtained.
