Divergence theorems in path space III: hypoelliptic diffusions and beyond

Details Divergence theorems in path space III: hypoelliptic diffusions and beyond Divergence theorems in path space III: hypoelliptic diffusions and beyond

2007-02-05

arxiv.org/abs/math/0702092v1

Mathematics

Probability

Scientific paper

Let $x$ denote a diffusion process defined on a closed compact manifold. In an earlier article, the author introduced a new approach to constructing admissible vector fields on the associated space of paths, under the assumption of ellipticity of $x$. In this article, this method is extended to yield similar results for degenerate diffusion processes. In particular, these results apply to non-elliptic diffusions satisfying H\"ormander's condition.

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