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Efficient simulation of nonlinear parabolic SPDEs with additive noise
Arnulf Jentzen, Peter Kloeden, Georg Winkel
Recently, in a paper by Jentzen and Kloeden [Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 465 (2009) 649-667], a new method for simulating nearly linear stochastic partial diff…
Loss of regularity for Kolmogorov equations
Martin Hairer, Martin Hutzenthaler, Arnulf Jentzen
The celebrated Hörmander condition is a sufficient (and nearly necessary) condition for a second-order linear Kolmogorov partial differential equation (PDE) with smooth coefficient…
Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients
Martin Hutzenthaler, Arnulf Jentzen
Many stochastic differential equations (SDEs) in the literature have a superlinearly growing nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the com…