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- W3025092902 abstract "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." @default.
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- W3025092902 date "2020-10-01" @default.
- W3025092902 modified "2023-10-17" @default.
- W3025092902 title "Solving linear parabolic rough partial differential equations" @default.
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- W3025092902 doi "https://doi.org/10.1016/j.jmaa.2020.124236" @default.
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