Self-intersection local time of an S '(R-d)-valued process involving motions of two types

We study existence and continuity of self-intersection local time (SILT) fo r a Gaussian L' (R-d)-valued process which arises as a high-density fluctua tion limit of a particle system in R-d, where the particle motion switches back and forth between symmetric stable processes of indices alpha(1) and a lpha(2) at exponential time intervals. We prove that SILT exists if and onl y if d < 2 min{alpha(1), alpha(2)}. This means that existence of SILT is de termined by the "most mobile" of the two types, and we interpret this resul t in terms of the particle picture. In contrast with the single-type case, there are technical difficulties due to the lack of self-similarity of the particle paths. (C) 1999 Published by Elsevier Science B.V. All rights rese rved.