Weak differentiability of solutions to SDEs with semi-monotone drifts

Document Type : Research Paper


1 Department of Applied Mathematics‎, ‎Faculty of Mathematical Sciences‎, ‎Tarbiat Modares University‎, ‎P.O‎. ‎Box 14115-134‎, ‎Tehran‎, ‎Iran

2 Graduate School of Management and Economics‎, ‎Sharif University of Technology‎, ‎P.O‎. ‎Box 11155-9415‎, ‎Tehran‎, ‎Iran


‎In this work we prove Malliavin differentiability for the solution to an SDE with locally Lipschitz and semi-monotone drift‎. ‎To prove this formula‎, ‎we construct a sequence of SDEs with globally Lipschitz drifts and show that the $p$-moments of their Malliavin derivatives are uniformly bounded‎.


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