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On hypoelliptic bridge. (English) Zbl 1345.60089
Summary: A conditioned hypoelliptic process on a compact manifold, satisfying the strong Hörmander condition, is a hypoelliptic bridge. If the Markov generator satisfies the two step strong Hörmander condition, the drift of the conditioned hypoelliptic bridge is integrable on \([0,1]\) and the hypoelliptic bridge is a continuous semi-martingale.

MSC:
60J60 Diffusion processes
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60J35 Transition functions, generators and resolvents
60G48 Generalizations of martingales
58J65 Diffusion processes and stochastic analysis on manifolds
58J70 Invariance and symmetry properties for PDEs on manifolds
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