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Regular version of the site

Article

Solving linear parabolic rough partial differential equations

Journal of Mathematical Analysis and Applications. 2020. Vol. 490. No. 1. P. 124236.
Bayer C., Belomestny D., Redmann M., Riedel S., Schoenmakers J.

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 1/3 < α ≤ 1/2. 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, we present a simulation study showing the applicability of the proposed algorithm.