Multilevel Picard approximations of high-dimensional semilinear partial differential equations with locally monotone coefficient functions

The full history recursive multilevel Picard approximation method for semilinear parabolic partial differential equations (PDEs) is the only method which provably overcomes the curse of dimensionality for general time horizons if the coefficient functions and the nonlinearity are globally Lipschitz...

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Vydáno v:Applied numerical mathematics Ročník 181; s. 151 - 175
Hlavní autoři: Hutzenthaler, Martin, Nguyen, Tuan Anh
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 01.11.2022
Témata:
Curse of dimensionality
High-dimensional PDEs
Locally monotone
Multilevel Monte Carlo method
Multilevel Picard approximations
Tamed Euler-type approximation
Multilevel Picard approximations
Curse of dimensionality
Multilevel Monte Carlo method
Locally monotone
Tamed Euler-type approximation
High-dimensional PDEs
ISSN:0168-9274, 1873-5460
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Shrnutí:The full history recursive multilevel Picard approximation method for semilinear parabolic partial differential equations (PDEs) is the only method which provably overcomes the curse of dimensionality for general time horizons if the coefficient functions and the nonlinearity are globally Lipschitz continuous and the nonlinearity is gradient-independent. In this article we extend this result to locally monotone coefficient functions. Our results cover a range of semilinear PDEs with polynomial coefficient functions.
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2022.05.009