Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cartan connections for stochastic developments on sub-Riemannian
  manifolds   Analogous to the characterisation of Brownian motion on a Riemannian manifold
as the development of Brownian motion on a Euclidean space, we construct
sub-Riemannian diffusions on equinilpotentisable sub-Riemannian manifolds by
developing a canonical stochastic process arising as the lift of Brownian
motion to an associated model space. The notion of stochastic development we
introduce for equinilpotentisable sub-Riemannian manifolds uses Cartan
connections, which take the place of the Levi-Civita connection in Riemannian
geometry. We first derive a general expression for the generator of the
stochastic process which is the stochastic development with respect to a Cartan
connection of the lift of Brownian motion to the model space. We further
provide a necessary and sufficient condition for the existence of a Cartan
connection which develops the canonical stochastic process to the
sub-Riemannian diffusion associated with the sub-Laplacian defined with respect
to the Popp volume. We illustrate the construction of a suitable Cartan
connection for free sub-Riemannian structures with two generators and we
discuss an example where the condition is not satisfied.

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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn