1.8k citations · 7.5k across the 146 of their papers we have counts for
9 papers · 1 filter
On the mild Itô formula in Banach spaces
Sonja Cox, Arnulf Jentzen, Ryan Kurniawan +1
The mild Ito formula proposed in Theorem 1 in [Da Prato, G., Jentzen, A., \& Röckner, M., A mild Ito formula for SPDEs, arXiv:1009.3526 (2012), To appear in the Trans.\ Amer.\ Math…
Weak convergence rates for numerical approximations of stochastic partial differential equations with nonlinear diffusion coefficients in UMD Banach spaces
Mario Hefter, Arnulf Jentzen, Ryan Kurniawan
Strong convergence rates for numerical approximations of semilinear stochastic partial differential equations (SPDEs) with smooth and regular nonlinearities are well understood in…
Regularity properties for solutions of infinite dimensional Kolmogorov equations in Hilbert spaces
Adam Andersson, Mario Hefter, Arnulf Jentzen +1
In this article we establish regularity properties for solutions of infinite dimensional Kolmogorov equations. We prove that if the nonlinear drift coefficients, the nonlinear diff…
On the differentiability of solutions of stochastic evolution equations with respect to their initial values
Adam Andersson, Arnulf Jentzen, Ryan Kurniawan +1
In this article we study the differentiability of solutions of parabolic semilinear stochastic evolution equations (SEEs) with respect to their initial values. We prove that if the…
Exponential moments for numerical approximations of stochastic partial differential equations
Arnulf Jentzen, Primož Pušnik
Stochastic partial differential equations (SPDEs) have become a crucial ingredient in a number of models from economics and the natural sciences. Many SPDEs that appear in such app…
Multilevel Picard iterations for solving smooth semilinear parabolic heat equations
Weinan E, Martin Hutzenthaler, Arnulf Jentzen +1
We introduce a new family of numerical algorithms for approximating solutions of general high-dimensional semilinear parabolic partial differential equations at single space-time p…