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We consider global pseudodifferential operators on symmetric spaces ofnoncompact type, defined using spherical functions. The associated symbols havea natural probabilistic form that extend the notion of the characteristicexponent appearing in Gangolli's L\'evy-Khinchine formula to a function of twovariables. The Hille-Yosida-Ray theorem is used to obtain conditions on such asymbol so that the corresponding pseudodifferential operator has an extensionthat generates a sub-Feller semigroup, generalising existing results forEuclidean space.

Sub-Feller Semigroups Generated by Pseudodifferential Operators on Symmetric Spaces of Noncompact Type