Level sets of multiparameter stable processes (Q877229)

Additive stable processes (here called multiparameter stable processes) are interesting as a toy model for stable sheets, which are much harder to study, and also come up naturally in the theory of intersections of stable processes. The present paper gives the precise Hausdorff gauge function for the zero set of additive stable processes satisfying Taylor's condition~(A), adding an upper bound to the lower bound of \textit{D. Khoshnevisan, Y. Xiao} and \textit{Y. Zhong} [Stochastic Processes Appl. 104, No. 2, 193--216 (2003; Zbl 1075.60520)]. In particular, this implies that the local time at zero is a constant multiple of the Hausdorff measure with respect to this gauge function.