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- Publications
- Influence

Runge-Kutta Methods for the Strong Approximation of Solutions of Stochastic Differential Equations

- A. Rößler
- Computer Science, Mathematics
- SIAM J. Numer. Anal.
- 1 July 2010

Some new stochastic Runge-Kutta (SRK) methods for the strong approximation of solutions of stochastic differential equations (SDEs) with improved efficiency are introduced. Their convergence is… Expand

Second Order Runge-Kutta Methods for Itô Stochastic Differential Equations

- A. Rößler
- Computer Science, Mathematics
- SIAM J. Numer. Anal.
- 1 April 2009

A new class of stochastic Runge-Kutta methods for the weak approximation of the solution of Ito stochastic differential equation systems with a multidimensional Wiener process is introduced. As the… Expand

Runge-Kutta methods for the numerical solution of stochastic differential equations

- A. Rößler
- Mathematics
- 2003

- 50
- 8

Iterated stochastic integrals in infinite dimensions: approximation and error estimates

- Claudine Leonhard, Andreas Rößler
- Mathematics
- 20 September 2017

Higher order numerical schemes for stochastic partial differential equations that do not possess commutative noise require the simulation of iterated stochastic integrals. In this work, we extend the… Expand

Rooted Tree Analysis for Order Conditions of Stochastic Runge-Kutta Methods for the Weak Approximation of Stochastic Differential Equations

- A. Rößler
- Mathematics
- 1 March 2006

Abstract A general class of stochastic Runge-Kutta methods for the weak approximation of Itô and Stratonovich stochastic differential equations with a multi-dimensional Wiener process is introduced.… Expand

Stochastic Taylor Expansions for the Expectation of Functionals of Diffusion Processes

- A. Rößler
- Mathematics
- 1 January 2004

Abstract Stochastic Taylor expansions of the expectation of functionals applied to diffusion processes which are solutions of stochastic differential equation systems are introduced. Taylor formulas… Expand

Runge–Kutta Methods for Itô Stochastic Differential Equations with Scalar Noise

- A. Rößler
- Mathematics
- 2 March 2006

A general class of stochastic Runge–Kutta methods for Itô stochastic differential equation systems w.r.t. a one-dimensional Wiener process is introduced. The colored rooted tree analysis is applied… Expand

Second order Runge–Kutta methods for Stratonovich stochastic differential equations

- A. Rößler
- Mathematics
- 12 May 2007

The weak approximation of the solution of a system of Stratonovich stochastic differential equations with a m–dimensional Wiener process is studied. Therefore, a new class of stochastic Runge–Kutta… Expand

Classification of stochastic Runge-Kutta methods for the weak approximation of stochastic differential equations

- K. Debrabant, A. Rößler
- Mathematics, Computer Science
- Math. Comput. Simul.
- 1 April 2008

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 Ito stochastic differential… Expand

Runge-Kutta methods for Stratonovich stochastic differential equation systems with commutative noise

- A. Rößler
- Mathematics
- 1 March 2004

A class of explicit stochastic Runge-Kutta (SRK) methods for Stratonovich stochastic differential equation systems w.r.t, m-dimensional Wiener processes satisfying a commutativity condition is… Expand