47 citations · 104 across the 15 of their papers we have counts for
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Nonlinear Monte Carlo methods with polynomial runtime for high-dimensional iterated nested expectations
Christian Beck, Arnulf Jentzen, Thomas Kruse
The approximative calculation of iterated nested expectations is a recurring challenging problem in applications. Nested expectations appear, for example, in the numerical approxim…
Overcoming the curse of dimensionality in the numerical approximation of high-dimensional semilinear elliptic partial differential equations
Christian Beck, Lukas Gonon, Arnulf Jentzen
Recently, so-called full-history recursive multilevel Picard (MLP) approximation schemes have been introduced and shown to overcome the curse of dimensionality in the numerical app…
Strong convergence rates on the whole probability space for space-time discrete numerical approximation schemes for stochastic Burgers equations
Martin Hutzenthaler, Arnulf Jentzen, Felix Lindner +1
The main result of this article establishes strong convergence rates on the whole probability space for explicit space-time discrete numerical approximations for a class of stochas…
Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations
Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse +2
For a long time it is well-known that high-dimensional linear parabolic partial differential equations (PDEs) can be approximated by Monte Carlo methods with a computational effort…
Counterexamples to regularities for the derivative processes associated to stochastic evolution equations
Mario Hefter, Arnulf Jentzen, Ryan Kurniawan
In the recent years there has been an increased interest in studying regularity properties of the derivatives of stochastic evolution equations (SEEs) with respect to their initial…
Taylor expansions of solutions of stochastic partial differential equations with additive noise
Arnulf Jentzen, Peter Kloeden
The solution of a parabolic stochastic partial differential equation (SPDE) driven by an infinite-dimensional Brownian motion is in general not a semi-martingale anymore and does i…