Absolute continuity under flows generated by SDE with measurable drift coefficients |
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| Authors: | Dejun Luo |
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| Affiliation: | UR Mathématiques, Université du Luxembourg, 6, rue Richard Coudenhove-Kalergi, L-1359, Luxembourg Key Lab of Random Complex Structures and Data Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China |
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| Abstract: | We consider the Itô SDE with a non-degenerate diffusion coefficient and a 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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| Keywords: | primary, 60H10 secondary, 34F05, 60J60 |
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