Bulletin of the Iranian Mathematical Society

Bulletin of the Iranian Mathematical Society

Weak differentiability of solutions to SDEs with semi-monotone drifts

Document Type : Research Paper

Authors
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
Abstract
‎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.
Keywords
Subjects

Volume 41, Issue 4 - Serial Number 4
August 2015
Pages 873-888

  • Receive Date 03 September 2013
  • Revise Date 19 February 2014
  • Accept Date 19 May 2014