104 citations · 382 across the 27 of their papers we have counts for
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Families of efficient second order Runge-Kutta methods for the weak approximation of Itô stochastic differential equations
Kristian Debrabant, Andreas Rößler
Recently, a new class of second order Runge-Kutta methods for Itô stochastic differential equations with a multidimensional Wiener process was introduced by Rößler. In contrast to…
Classification of Stochastic Runge-Kutta Methods for the Weak Approximation of Stochastic Differential Equations
Kristian Debrabant, Andreas Rößler
In the present paper, a class of stochastic Runge-Kutta methods containing the second order stochastic Runge-Kutta scheme due to E. Platen for the weak approximation of Itô stochas…
Continuous Weak Approximation for Stochastic Differential Equations
Kristian Debrabant, Andreas Rößler
A convergence theorem for the continuous weak approximation of the solution of stochastic differential equations by general one step methods is proved, which is an extension of a t…
Convergence of Runge-Kutta Methods Applied to Linear Partial Differential-Algebraic Equations
Kristian Debrabant, Karl Strehmel
We apply Runge-Kutta methods to linear partial differential-algebraic equations of the form , where and th…
On quasi-linear PDAEs with convection: applications, indices, numerical solution
Wenfried Lucht, Kristian Debrabant
For a class of partial differential algebraic equations (PDAEs) of quasi-linear type which include nonlinear terms of convection type a possibility to determine a time and spatial…
Diagonally drift-implicit Runge-Kutta methods of weak order one and two for Itô SDEs and stability analysis
Kristian Debrabant, Andreas Rößler
The class of stochastic Runge-Kutta methods for stochastic differential equations due to Rößler is considered. Coefficient families of diagonally drift-implicit stochastic Runge-Ku…
Analysis of multilevel Monte Carlo path simulation using the Milstein discretisation
Michael B. Giles, Kristian Debrabant, Andreas Rößler
The multilevel Monte Carlo path simulation method introduced by Giles ({\it Operations Research}, 56(3):607-617, 2008) exploits strong convergence properties to improve the computa…
On the Acceleration of the Multi-Level Monte Carlo Method
Kristian Debrabant, Andreas Rößler
The multi-level Monte Carlo method proposed by M. Giles (2008) approximates the expectation of some functionals applied to a stochastic process with optimal order of convergence fo…