Local time for stable moving average processes: Hِlder conditions

The Fourier analytic approach due to S.M. Berman is considered for a certain class of α-stable moving average processes, 1 < α ≤ 2. It is proved that the local times of such processes satisfy a uniform Hölder condition of order |Q|1 − 1α| log|Q||1α for small intervals Q. A decomposition of a stable moving average 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 Bermanʹs integral is compared to the LND method.