Solving Kolmogorov PDEs without the curse of dimensionality via deep learning and asymptotic expansion with Malliavin calculus
A Takahashi, T Yamada - Partial Differential Equations and Applications, 2023 - Springer
This paper proposes a new spatial approximation method without the curse of
dimensionality for solving high-dimensional partial differential equations (PDEs) by using an …
dimensionality for solving high-dimensional partial differential equations (PDEs) by using an …
A new algorithm for computing path integrals and weak approximation of SDEs inspired by large deviations and Malliavin calculus
T Yamada - Applied Numerical Mathematics, 2023 - Elsevier
The paper gives a novel path integral formula inspired by large deviation theory and
Malliavin calculus. The proposed finite-dimensional approximation of integrals on path …
Malliavin calculus. The proposed finite-dimensional approximation of integrals on path …
A weak approximation method for irregular functionals of hypoelliptic diffusions
N Akiyama, T Yamada - Applied Numerical Mathematics, 2022 - Elsevier
The paper introduces a new weak approximation scheme for Kolmogorov type hypoelliptic
diffusions based on an operator splitting method and a Malliavin calculus approach. The …
diffusions based on an operator splitting method and a Malliavin calculus approach. The …
[PDF][PDF] Asymptotic expansion and deep neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential …
A Takahashi, T Yamda - 2022 - carf.eu-tokyo.ac.jp
This paper proposes a new spatial approximation method without the curse of
dimensionality for solving high-dimensional partial differential equations (PDEs) by using an …
dimensionality for solving high-dimensional partial differential equations (PDEs) by using an …
Weak approximation of SDEs for tempered distributions and applications
Y Iguchi, T Yamada - Advances in Computational Mathematics, 2022 - Springer
The paper shows a new weak approximation for generalized expectation of composition of a
Schwartz tempered distribution and a solution to stochastic differential equation. Any order …
Schwartz tempered distribution and a solution to stochastic differential equation. Any order …