On hypoelliptic bridge. (English) Zbl 1345.60089

Li, Xue-Mei

Electron. Commun. Probab. 21, Paper No. 24, 12 p. (2016).

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

Keywords:

hypoelliptic bridges; Markov generator; compact manifold; strong Hörmander condition; adjoint process; hypoelliptic kernel; semi-martingale