Spectral conditions for local nondeterminism

Let X(t) be a real Gaussian process with stationary increments and spectral distribution function F(x). Put [phi](t)=F([infinity]) - F(1/t). Sufficient conditions in terms of F are given for the process to be locally [phi]-nondeterministic. These are formulated for discrete and absolutely continuous functions F. The results in the discrete case are applied to the analysis of the local time of a random Fourier series with i.i.d. coefficients. The class of distributions of the coefficients includes not only the normal distribution but others such as the symmetric stable distribution.