null
(Ed.)
Existence and uniqueness results for solutions of stochastic differential
equations (SDEs) under exceptionally weak conditions are
well known in the case where the diffusion coeffcient is nondegenerate.
Here, existence and uniqueness of strong solutions is obtained
in the case of degenerate SDEs in a class that is motivated by
diffusion representations for solutions of Schrödinger initial value
problems. In such examples, the dimension of the range of the
diffusion coeffcient is exactly half that of the state. In addition to
this degeneracy, two types of discontinuities and singularities in the
drift are allowed, where these are motivated by the structure of the
Coulomb potential. The first type consists of discontinuities that
may occur on a possibly high-dimensional manifold. The second
consists of singularities that may occur on a smoothly parameterized
curve.
more »
« less
Full Text Available