Transition density estimates for stable processes on symmetric spaces
The authors obtain exact upper and lower estimates for transition densities of \(\alpha\)-stable processes on Riemannian symmetric spaces of noncompact type. These processes are defined by a subordination procedure [\textit{R. K. Getoor}, Pac. J. Math. 11, 1287--1308 (1961; Zbl 0124.34502)], and their scaling properties were not known. The above estimates possess certain scaling properties, which can be interpreted as weak scaling properties of the processes themselves. Earlier, some estimates for the above transition densities were found for \(\alpha =1\) [\textit{J.-P. Anker} and \textit{L. Ji}, Geom. Funct. Anal. 9, No. 6, 1035--1091 (1999; Zbl 0942.43005)]; large time estimates were known in the rank one case [\textit{J.-C. Gruet}, Ann. Math. Blaise Pascal 5, No. 2, 39--48 (1998; Zbl 0926.60020)].
scientific article; zbMATH DE number 2164608