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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…
Ecological and genetic effects of introduced species on their native competitors
Meike J. Wittmann, Martin Hutzenthaler, Wilfried Gabriel +1
Species introductions to new habitats can cause a decline in the population size of competing native species and consequently also in their genetic diversity. We are interested in…
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…