Generalized stochastic flow associated to the Itô SDE with partially Sobolev coefficients and applications

Details Generalized stochastic flow associated to the Itô SDE with partially Sobolev coefficients and applications Generalized stochastic flow associated to the Itô SDE with partially Sobolev coefficients and applications

2012-03-20

arxiv.org/abs/1203.4405v2

Mathematics

Probability

41 pages. The proofs of Propositions 2.13 and 2.14 are slightly modified

Scientific paper

We consider the It\^o SDE with partially Sobolev coefficients. Under some
suitable conditions, we show the existence, uniqueness and stability of
generalized stochastic flows associated to such an equation. As an application,
we prove the weak differentiability of the stochastic flow generated by the
It\^o SDE with Sobolev coefficients.

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