Absolute continuity under flows generated by SDE with measurable drift coefficient

Details Absolute continuity under flows generated by SDE with measurable drift coefficient Absolute continuity under flows generated by SDE with measurable drift coefficient

2010-09-28

arxiv.org/abs/1009.5525v1

Mathematics

Probability

22 pages

Scientific paper

We consider the It\^{o} SDE with non-degenerate diffusion coefficient and measurable drift coefficient. Under the condition that the gradient of the diffusion coefficient and the divergences of the diffusion and drift coefficients are exponentially integrable with respect to the Gaussian measure, we show that the stochastic flow leaves the reference measure absolutely continuous.

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