TL;DR
This paper proves that under the two-step strong Hörmander condition, the hypoelliptic bridge is a continuous semi-martingale satisfying an integral bound, advancing understanding of conditioned hypoelliptic diffusions.
Contribution
It establishes the semi-martingale property and integral bounds for hypoelliptic bridges under the two-step Hörmander condition, a novel result in stochastic analysis.
Findings
Hypoelliptic bridges are continuous semi-martingales.
They satisfy specific integral bounds.
The results depend on the two-step strong Hörmander condition.
Abstract
We prove that if the Markov generator of a diffusion process satisfies the two step strong H\"ormander condition, the conditioned hypoelliptic bridge satisfies an integral bound and is a continuous semi-martingale.
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