Multilevel Monte Carlo method with applications to stochastic partial differential equations
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Date
2012
Publication Type
Journal Article
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yes
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Abstract
In this work, the approximation of Hilbert-space-valued random variables is combined with the approximation of the expectation by a multilevel Monte Carlo (MLMC) method. The number of samples on the different levels of the multilevel approximation are chosen such that the errors are balanced. The overall work then decreases in the optimal case to $O(h^-$$^2)$ if $h$ is the error of the approximation. The MLMC method is applied to functions of solutions of parabolic and hyperbolic stochastic partial differential equations as needed, for example, for option pricing. Simulations complete the paper.
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published
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Journal / series
Volume
89 (18)
Pages / Article No.
2479 - 2498
Publisher
Taylor & Francis
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Subject
Multilevel Monte Carlo; Stochastic partial differential equations; Stochastic finite element methods; Stochastic parabolic equation; Stochastic hyperbolic equation; Multilevel approximations
Organisational unit
03435 - Schwab, Christoph / Schwab, Christoph
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