48 citations · 151 across the 14 of their papers we have counts for
3 papers · 1 filter
Deep neural network approximations for Monte Carlo algorithms
Philipp Grohs, Arnulf Jentzen, Diyora Salimova
Recently, it has been proposed in the literature to employ deep neural networks (DNNs) together with stochastic gradient descent methods to approximate solutions of PDEs. There are…
Strong and weak divergence of exponential and linear-implicit Euler approximations for stochastic partial differential equations with superlinearly growing nonlinearities
Matteo Beccari, Martin Hutzenthaler, Arnulf Jentzen +3
The explicit Euler scheme and similar explicit approximation schemes (such as the Milstein scheme) are known to diverge strongly and numerically weakly in the case of one-dimension…
Existence, uniqueness, and numerical approximations for stochastic Burgers equations
Sara Mazzonetto, Diyora Salimova
In this paper we propose an all-in-one statement which includes existence, uniqueness, regularity, and numerical approximations of mild solutions for a class of stochastic partial…