Higher-order deep solver of non-linear PDEs implied by a non-linear discrete Clark-Ocone formula
Author:
Affiliation:
1. Department of Mathematical Sciences, Ritsumeikan University
Publisher
The Japan Society for Industrial and Applied Mathematics
Subject
General Engineering
Link
https://www.jstage.jst.go.jp/article/jsiaml/14/0/14_9/_pdf
Reference8 articles.
1. 1) W. E, J. Han and A. Jentzen, Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations, Commun. Math. Stat., 5 (2017), 349-380.
2. 2) D. Belomestny, S. Häfner, T. Nagapetyan and M. Urusov, Variance reduction for discretized diffusions via regression, J. Math. Anal. Appl., 458 (2018), 393-418.
3. 3) M. Sabate-Vidales, D. Siska and L. Szpruch, Unbiased deep solvers for parametric PDEs, arXiv:1810.05094 [q-fin.CP].
4. 4) J. Akahori, T. Amaba and K. Okuma, A discrete-time Clark--Ocone formula and its application to an error analysis, J. Theor. Probab., 30 (2017), 932-960.
5. 5) D. Nualart, The Malliavin Calculus and Related Topics, 2nd edn., Springer-Verlag, Berlin, 2006.
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1. An asymptotic expansion of the solution of a semi-linear partial differential equation implied by a nonlinear Feynman–Kac formula;International Journal of Mathematics for Industry;2024-02-22
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