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Existence and uniqueness properties for solutions of a class of Banach space valued evolution equations
Arnulf Jentzen, Sara Mazzonetto, Diyora Salimova
In this note we provide a self-contained proof of an existence and uniqueness result for a class of Banach space valued evolution equations with an additive forcing term. The frame…
Exponential moment bounds and strong convergence rates for tamed-truncated numerical approximations of stochastic convolutions
Arnulf Jentzen, Felix Lindner, Primož Pušnik
In this article we establish exponential moment bounds, moment bounds in fractional order smoothness spaces, a uniform Hölder continuity in time, and strong convergence rates for a…
On the Itô-Alekseev-Gröbner formula for stochastic differential equations
Anselm Hudde, Martin Hutzenthaler, Arnulf Jentzen +1
In this article we establish a new formula for the difference of a test function of the solution of a stochastic differential equation and of the test function of an Itô process. T…
Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations
Sebastian Becker, Benjamin Gess, Arnulf Jentzen +1
Optimal upper and lower error estimates for strong full-discrete numerical approximations of the stochastic heat equation driven by space-time white noise are obtained. In particul…
On the Alekseev-Gröbner formula in Banach spaces
Arnulf Jentzen, Felix Lindner, Primož Pušnik
The Alekseev-Gröbner formula is a well known tool in numerical analysis for describing the effect that a perturbation of an ordinary differential equation (ODE) has on its solution…
DNN Expression Rate Analysis of High-dimensional PDEs: Application to Option Pricing
Dennis Elbrächter, Philipp Grohs, Arnulf Jentzen +1
We analyze approximation rates by deep ReLU networks of a class of multi-variate solutions of Kolmogorov equations which arise in option pricing. Key technical devices are deep ReL…