TY - JOUR
T1 - Pathwise definition of second-order SDEs
AU - Quer-Sardanyons, Lluís
AU - Tindel, Samy
PY - 2012/2/1
Y1 - 2012/2/1
N2 - 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.
AB - 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.
KW - Elliptic SPDEs
KW - Fractional Brownian motion
KW - Malliavin calculus
KW - Young integration
U2 - 10.1016/j.spa.2011.08.014
DO - 10.1016/j.spa.2011.08.014
M3 - Article
SN - 0304-4149
VL - 122
SP - 466
EP - 497
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
ER -