Quasi-Regression Monte-Carlo Scheme for Semi-Linear PDEs and BSDEs with Large Scale Parallelization on GPUs
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Quasi-Regression Monte-Carlo Scheme for Semi-Linear PDEs and BSDEs with Large Scale Parallelization on GPUsData
2019-04-04Cita bibliográfica
Gobet, E., López-Salas, J.G. & Vázquez, C. Quasi-Regression Monte-Carlo Scheme for Semi-Linear PDEs and BSDEs with Large Scale Parallelization on GPUs. Arch Computat Methods Eng 27, 889–921 (2020). https://doi.org/10.1007/s11831-019-09335-x
Resumo
[Abstract]: In this article we design a novel quasi-regression Monte Carlo algorithm in order to approximate the solution of discrete time backward stochastic differential equations, and we analyze the convergence of the proposed method. The algorithm also approximates the solution to the related semi-linear parabolic partial differential equation obtained through the well known Feynman–Kac representation. For the sake of enriching the algorithm with high order convergence a weighted approximation of the solution is computed and appropriate conditions on the parameters of the method are inferred. With the challenge of tackling problems in high dimensions we propose suitable projections of the solution and efficient parallelizations of the algorithm taking advantage of powerful many core processors such as graphics processing units.
Palabras chave
Backward stochastic differential equations
High-order convergence
Linear-parabolic
Many-core processors
Monte carlo algorithms
Monte carlo schemes
Parallel computing
GPUs
High-order convergence
Linear-parabolic
Many-core processors
Monte carlo algorithms
Monte carlo schemes
Parallel computing
GPUs
Descrición
©2019 This version of the article has been accepted for publication, after
peer review and is subject to Springer Nature’s AM terms of use, but is not
the Version of Record and does not reflect post-acceptance improvements,
or any corrections. The Version of Record is available online at:
https://doi.org/10.1007/s11831-019-09335-x
Versión do editor
ISSN
1886-1784
1134-3060
1134-3060