4 papers · 1 filter
Stochastic evolution equations driven by arbitrary cylindrical Lévy processes
Gergely Bodó, Sonja Cox, Adam Jakubowski +1
We establish the first existence and uniqueness result for mild solutions of abstract stochastic evolution equations driven by arbitrary cylindrical Lévy processes in Hilbert spac…
Universal approximation by signatures for infinite-dimensional rough paths
Sonja Cox, Asma Khedher, Thijs Maessen
We establish universal approximation theorems for infinite-dimensional geometric rough paths, i.e., we show that continuous functions on the space of infinite-dimensional weakly ge…
Weak convergence rates for temporal numerical approximations of stochastic wave equations with multiplicative noise
Sonja Cox, Arnulf Jentzen, Felix Lindner
In this work we establish weak convergence rates for temporal discretisations of stochastic wave equations with multiplicative noise, in particular, for the hyperbolic Anderson mod…
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…