SELF-INTERSECTIONS AND LOCAL NONDETERMINISM OF GAUSSIAN-PROCESSES

Let X(t), t greater-than-or-equal-to 0, be a vector Gaussian process in R(m) whose components are i.i.d. copies of a real Gaussian process X(t) with stationary increments. Under specified conditions on the spectral distribution function used in the representation of the incremental variance function, it is shown that the self-intersection local time of multiplicity r of the vector process is jointly continuous. The dimension of the self-intersection set is estimated from above and below. The main tool is the concept of local nondeterminism.