LOCAL TIME FOR STABLE MOVING AVERAGE PROCESSES - HOLDER CONDITIONS

The Fourier analytic approach due to S.M. Berman is considered for a c ertain class of alpha-stable moving average processes, 1 < alpha less than or equal to 2. It is proved that the local times of such processe s satisfy a uniform Holder condition of order \Q\(1-1/alpha)\ log\Q\\( 1/alpha) for small intervals e. A decomposition of a stable moving ave rage process into a part with jointly continuous local time and a part with smooth sample paths is given and the direct method of evaluation of Berman's integral is compared to the LND method.