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Existence, uniqueness, and regularity for stochastic evolution equations with irregular initial values
Adam Andersson, Arnulf Jentzen, Ryan Kurniawan
In this article we develop a framework for studying parabolic semilinear stochastic evolution equations (SEEs) with singularities in the initial condition and singularities at the…
Weak convergence rates for spatial spectral Galerkin approximations of semilinear stochastic wave equations with multiplicative noise
Ladislas Jacobe de Naurois, Arnulf Jentzen, Timo Welti
Stochastic wave equations appear in several models for evolutionary processes subject to random forces, such as the motion of a strand of DNA in a liquid or heat flow around a ring…
On stochastic differential equations with arbitrary slow convergence rates for strong approximation
Arnulf Jentzen, Thomas Müller-Gronbach, Larisa Yaroslavtseva
In the recent article [Hairer, M., Hutzenthaler, M., Jentzen, A., Loss of regularity for Kolmogorov equations, Ann. Probab. 43 (2015), no. 2, 468--527] it has been shown that there…
Strong convergence rates for an explicit numerical approximation method for stochastic evolution equations with non-globally Lipschitz continuous nonlinearities
Arnulf Jentzen, Primož Pušnik
In this article we propose a new, explicit and easily implementable numerical method for approximating a class of semilinear stochastic evolution equations with non-globally Lipsch…
Weak convergence rates for Euler-type approximations of semilinear stochastic evolution equations with nonlinear diffusion coefficients
Arnulf Jentzen, Ryan Kurniawan
Strong convergence rates for time-discrete numerical approximations of semilinear stochastic evolution equations (SEEs) with smooth and regular nonlinearities are well understood i…