A Brownian SDE with merely measurable, Markovian drift is claimed to have a unique strong solution and H-C regular solution map whenever its Girsanov density has a finite L^{1+ε} moment.
Analysis on Wiener Space and Applications
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The aim of this book is to give a rigorous introduction for the graduate students to Analysis on Wiener space, a subject which has grown up very quickly these recent years under the new impulse of the Stochastic Calculus of Variations of Paul Malliavin.
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Strong solutions of SDE's with rough coefficients
A Brownian SDE with merely measurable, Markovian drift is claimed to have a unique strong solution and H-C regular solution map whenever its Girsanov density has a finite L^{1+ε} moment.