Stochastic sub-Riemannian geodesics on the Grushin distribution
نویسندگان
چکیده
Recent years have seen intensive scientific activities of describing diffusion processes with Brownian covariance given by a Riemannian metric on a manifold. In our paper the dynamics is specified through a stochastic variational principle for a generalization of the classical action, with a given kinetic Riemannian metric. In short, we introduce the concept of stochastic sub-Riemannian geodesics and find their equations in the case of Grushin distribution. We also discuss the number of stochastic geodesics between any two given points and calculate their energies. M.S.C. 2010: Primary: 93E20; Secondary: 93B05, 49J15.
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تاریخ انتشار 2014