Publications

Raphael Kruse, Nick Polydorides, Yue Wu (2019). Application of Randomized Quadrature Formulas to the Finite Element Method for Elliptic Equations. ArXiv Preprint.

Raphael Kruse, Yue Wu (2019). A randomized Milstein method for stochastic differential equations with non-differentiable drift coefficients. Discrete & Continuous Dynamical Systems - Ser. B, vol. 24(8), 3475-3502.

Monika Eisenmann, Mihály Kovács, Raphael Kruse, Stig Larsson (2019). Error Estimates of the Backward Euler-Maruyama Method for Multi-Valued Stochastic Differential Equations. ArXiv Preprint.

Monika Eisenmann, Raphael Kruse (2019). Two quadrature rules for stochastic Itô-integrals with fractional Sobolev regularity. Communications in Mathematical Sciences, vol. 16(8), 2125-2146.

Raphael Kruse, Yue Wu (2019). A randomized and fully discrete Galerkin finite element method for semilinear stochastic evolution equations. Mathematics of Computation, vol. 88, 2793-2825.

Monika Eisenmann, Mihály Kovács, Raphael Kruse, Stig Larsson (2019). On a randomized backward Euler method for nonlinear evolution equations with time-irregular coefficients. Foundations of Computational Mathematics, vol. 19, 1387-1430.

Raphael Kruse, Michael Scheutzow (2018). A discrete stochastic Gronwall lemma. Mathematics and Computers in Simulation, vol. 143, 149-157.

Raphael Kruse, Yue Wu (2017). Error analysis of randomized Runge-Kutta methods for differential equations with time-irregular coefficients. Computational Methods in Applied Mathematics, vol. 17(3), 479-498.

Wolf-Jürgen Beyn, Elena Isaak, Raphael Kruse (2017). Stochastic C-stability and B-consistency of explicit and implicit Milstein-type schemes. Journal of Scientific Computing, vol. 70, 1042-1077.

Adam Andersson, Raphael Kruse (2017). Mean-square convergence of the BDF2-Maruyama and backward Euler schemes for SDE satisfying a global monotonicity condition. BIT Numerical Mathematics, vol. 57, 21-53.

Wolf-Jürgen Beyn, Elena Isaak, Raphael Kruse (2016). Stochastic C-stability and B-consistency of explicit and implicit Euler-type schemes. Journal of Scientific Computing, vol. 67, 955-987.

Adam Andersson, Raphael Kruse, Stig Larsson (2016). Duality in refined Sobolev-Malliavin spaces and weak approximation of SPDE. Stochastics and Partial Differential Equations: Analysis and Computations, vol. 4, 113-149.

Raphael Kruse (2014). Consistency and stability of a Milstein-Galerkin finite element scheme for semilinear SPDE. Stochastic Partial Differential Equations: Analysis and Computations, vol. 2, 471-516.

Preprint PDF DOI

Raphael Kruse (2014). Strong and Weak Approximation of Semilinear Stochastic Evolution Equations. Lecture Notes in Mathematics, vol. 2093, Springer, Cham.

Raphael Kruse (2014). Optimal error estimates of Galerkin finite element methods for stochastic partial differential equations with multiplicative noise. IMA Journal of Numerical Analysis, vol. 34(1), 217-251.

Raphael Kruse, Stig Larsson (2012). Optimal regularity for semilinear stochastic partial differential equations with multiplicative noise. Electronic Journal of Probability, vol. 17, no. 65, 19 pp.

Preprint PDF DOI

Raphael Kruse (2012). Characterization of bistability for stochastic multistep methods. BIT Numerical Mathematics, vol. 52, 109-140.

Wolf-Jürgen Beyn, Raphael Kruse (2010). Two-sided error estimates for the stochastic theta method. Discrete & Continuous Dynamical Systems - Ser. B, vol. 24(2), 389-407.

Raphael Kruse (2010). Discrete approximation of stochastic differential equations. SeMA Journal, vol. 51, 83-90.