Pathwise definition of second-order SDEs

  • Quer-Sardanyons L
  • Tindel S
  • 3


    Mendeley users who have this article in their library.
  • 1


    Citations of this article.


In this article, a class of second-order differential equations on [0,1], driven by a γ-Hölder continuous function for any value of γ∈(0,1) and with multiplicative noise, is considered. We first show how to solve this equation in a pathwise manner, thanks to Young integration techniques. We then study the differentiability of the solution with respect to the driving process and consider the case where the equation is driven by a fractional Brownian motion, with two aims in mind: show that the solution that we have produced coincides with the one which would be obtained with Malliavin calculus tools, and prove that the law of the solution is absolutely continuous with respect to the Lebesgue measure. © 2011 Elsevier B.V. All rights reserved.

Author-supplied keywords

  • Elliptic SPDEs
  • Fractional Brownian motion
  • Malliavin calculus
  • Young integration

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document


  • Lluís Quer-Sardanyons

  • Samy Tindel

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free