Solving linear parabolic rough partial differential equations
- Bayer, Christian
- Belomestny, Denis
- Redmann, Martin
- Riedel, Sebastian
- Schoenmakers, John G. M.
2010 Mathematics Subject Classification
- 65C30 65C05 60H15
- Rough paths, rough partial differential equations, Feynman-Kac formula, regression
We study linear rough partial differential equations in the setting of [Friz and Hairer, Springer, 2014, Chapter 12]. More precisely, we consider a linear parabolic partial differential equation driven by a deterministic rough path W of Hölder regularity α with ⅓ < α ≤ ½ . Based on a stochastic representation of the solution of the rough partial differential equation, we propose a regression Monte Carlo algorithm for spatio-temporal approximation of the solution. We provide a full convergence analysis of the proposed approximation method which essentially relies on the new bounds for the higher order derivatives of the solution in space. Finally, a comprehensive simulation study showing the applicability of the proposed algorithm is presented.