Spectral conditions for local nondeterminism (Q1096248)

The concept of local nondeterminism and local time of Gaussian processes was introduced by the author in Indiana Univ. Math. J. 23, 69-94 (1973; Zbl 0264.60024). It was extended to local \(\phi\)-nondeterminism by \textit{J. Cuzick}, Ann. Probab. 6, 72-84 (1978; Zbl 0374.60051). Let X(t), \(t\geq 0)\), be a Gaussian process with mean 0 and stationary increments. Let \(\phi (t)=F(\infty)-F(1/t)\), \(t>0\), where F is the spectral distribution function of X(t). Sufficient conditions in terms of F (F can be discrete or absolutely continuous) are derived for the local \(\phi\)-nondeterminism of X(t) and for the existence of the local time. The results are applied for random Fourier series with i.i.d. coefficients, which may have e.g. symmetric stable distributions.