3 papers
math.NA2025
Full history recursive multilevel Picard approximations suffer from the curse of dimensionality for the Hamilton-Jacobi-Bellman equation of a stochastic control problem
Martin Hutzenthaler, Tuan Anh Nguyen
Full history recursive multilevel Picard (MLP) approximations have been proved to overcome the curse of dimensionality in the numerical approximation of semilinear heat equations w…
math.PR2024
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.…
math.PR2024
Local Lipschitz continuity in the initial value and strong completeness for nonlinear stochastic differential equations
Sonja Cox, Martin Hutzenthaler, Arnulf Jentzen
Recently, Hairer et. al (2012) showed that there exist SDEs with infinitely often differentiable and globally bounded coefficient functions whose solutions fail to be locally Lipsc…