Absolute continuity under flows generated by SDE with measurable drift coefficients
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.
Volume (Year): 121 (2011)
Issue (Month): 10 (October)
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- Zhang, Xicheng, 2005. "Strong solutions of SDES with singular drift and Sobolev diffusion coefficients," Stochastic Processes and their Applications, Elsevier, vol. 115(11), pages 1805-1818, November.
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