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.

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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
  • First Publish Date: 01 August 2015