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Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Doi
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 with 1=3 < 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, a comprehensive
simulation study showing the applicability of the proposed algorithm is
presented
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