A Microlocal Analysis of the L\'evy Generator with Conjugate Points
Mathematics, Differential Geometry, Differential Geometry (math.DG), Probability (math.PR)
We analyze the microlocal structure of the infinitesimal generator of a L\'evy process on a closed Riemannian manifold when conjugate points are allowed. We show that if there are no singular conjugate pairs, then the infinitesimal generator can be written as a sum of pseudodifferential operators and Fourier integral operators. This extends and unifies known results for the flat torus, the sphere, and Anosov manifolds.