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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 isExpand
  • 92
  • 13
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 theExpand
  • 58
  • 9
Iterated stochastic integrals in infinite dimensions: approximation and error estimates
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 theExpand
  • 10
  • 5
Rooted Tree Analysis for Order Conditions of Stochastic Runge-Kutta Methods for the Weak Approximation of Stochastic Differential Equations
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
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  • 4
Stochastic Taylor Expansions for the Expectation of Functionals of Diffusion Processes
Abstract Stochastic Taylor expansions of the expectation of functionals applied to diffusion processes which are solutions of stochastic differential equation systems are introduced. Taylor formulasExpand
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  • 4
Runge–Kutta Methods for Itô Stochastic Differential Equations with Scalar Noise
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 appliedExpand
  • 41
  • 3
Second order Runge–Kutta methods for Stratonovich stochastic differential equations
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–KuttaExpand
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  • 3
Classification of stochastic Runge-Kutta methods for the weak approximation of stochastic differential equations
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 differentialExpand
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  • 3
Runge-Kutta methods for Stratonovich stochastic differential equation systems with commutative noise
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 isExpand
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  • 3