We consider the class of stationary-increment harmonizable stable processes with infinite control measure, which most notably includes real harmonizable fractional stable motions. We give conditions for the integrability of the paths of such processes with respect to a finite, absolutely continuous measure and derive the distributional characteristics of the path integral with respect to said measure. The convolution of the path of a stationary-increment harmonizable stable process with a suitable measure yields a real stationary harmonizable stable process with finite control measure. This allows us to construct consistent estimators for the index of stability as well as the kernel function in the integral representation of a stationary increment harmonizable stable process (up to a constant factor). For real harmonizable fractional stable motions consistent estimators for the index of stability and its Hurst parameter are given. These are computed directly from the periodogram frequency estimates of the smoothed process.

翻译：本文研究一类具有无限控制测度的平稳增量可调和稳定过程，其中最重要的特例是实可调和分数稳定运动。我们给出了此类过程路径关于有限绝对连续测度的可积性条件，并推导了路径关于该测度积分的分布特性。将平稳增量可调和稳定过程的路径与适当测度进行卷积，可得到具有有限控制测度的实平稳可调和稳定过程。基于此，我们为平稳增量可调和稳定过程的稳定性指数及其积分表示中的核函数（至常数因子）构造了一致估计量。针对实可调和分数稳定运动，我们给出了稳定性指数及其Hurst参数的一致估计量。这些估计量直接通过平滑化过程的周期图频率估计计算得到。