[图书][B] A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black–Scholes partial differential equations
Artificial neural networks (ANNs) have very successfully been used in numerical simulations
for a series of computational problems ranging from image classification/image recognition …
for a series of computational problems ranging from image classification/image recognition …
Solving the Kolmogorov PDE by means of deep learning
Stochastic differential equations (SDEs) and the Kolmogorov partial differential equations
(PDEs) associated to them have been widely used in models from engineering, finance, and …
(PDEs) associated to them have been widely used in models from engineering, finance, and …
On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients
M Hutzenthaler, A Jentzen - The Annals of Probability, 2020 - JSTOR
We develop a perturbation theory for stochastic differential equations (SDEs) by which we
mean both stochastic ordinary differential equations (SODEs) and stochastic partial …
mean both stochastic ordinary differential equations (SODEs) and stochastic partial …
Strong convergence rates of semidiscrete splitting approximations for the stochastic Allen–Cahn equation
This article analyses an explicit temporal splitting numerical scheme for the stochastic Allen–
Cahn equation driven by additive noise in a bounded spatial domain with smooth boundary …
Cahn equation driven by additive noise in a bounded spatial domain with smooth boundary …
Global convergence of stochastic gradient hamiltonian monte carlo for nonconvex stochastic optimization: Nonasymptotic performance bounds and momentum-based …
Stochastic gradient Hamiltonian Monte Carlo (SGHMC) is a variant of stochastic gradients
with momentum where a controlled and properly scaled Gaussian noise is added to the …
with momentum where a controlled and properly scaled Gaussian noise is added to the …
Nonasymptotic estimates for stochastic gradient Langevin dynamics under local conditions in nonconvex optimization
In this paper, we are concerned with a non-asymptotic analysis of sampling algorithms used
in nonconvex optimization. In particular, we obtain non-asymptotic estimates in Wasserstein …
in nonconvex optimization. In particular, we obtain non-asymptotic estimates in Wasserstein …
Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks
Parabolic partial differential equations (PDEs) are widely used in the mathematical modeling
of natural phenomena and man-made complex systems. In particular, parabolic PDEs are a …
of natural phenomena and man-made complex systems. In particular, parabolic PDEs are a …
[HTML][HTML] Strong convergence rate of finite difference approximations for stochastic cubic Schrödinger equations
In this paper, we derive a strong convergence rate of spatial finite difference approximations
for both focusing and defocusing stochastic cubic Schrödinger equations driven by a …
for both focusing and defocusing stochastic cubic Schrödinger equations driven by a …
[HTML][HTML] Strong convergence rate of splitting schemes for stochastic nonlinear Schrödinger equations
In this paper, we show that solutions of stochastic nonlinear Schrödinger (NLS) equations
can be approximated by solutions of coupled splitting systems. Based on these systems, we …
can be approximated by solutions of coupled splitting systems. Based on these systems, we …
A positivity preserving Lamperti transformed Euler–Maruyama method for solving the stochastic Lotka–Volterra competition model
Y Li, W Cao - Communications in Nonlinear Science and Numerical …, 2023 - Elsevier
A new positivity preserving numerical scheme is presented for a class of d-dimensional
stochastic Lotka–Volterra competitive models, which are characterized by super-linear …
stochastic Lotka–Volterra competitive models, which are characterized by super-linear …