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Original Articles

Stochastic Taylor Expansions: Weight Functions of B-Series Expressed as Multiple Integrals

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Pages 293-302 | Received 19 May 2009, Accepted 01 Jun 2009, Published online: 01 Feb 2010

References

  • Burrage , K. , and Burrage , P.M. 1996 . High strong order explicit Runge–Kutta methods for stochastic ordinary differential equations . Applied Numerical Mathematics 22 ( 1–3 ): 81 – 101 .
  • Burrage , K. , and Burrage , P.M. 1998 . General order conditions for stochastic Runge–Kutta methods for both commuting and non-commuting stochastic ordinary differential equation systems . Applied Numerical Mathematics 28 ( 2–4 ): 161 – 177 .
  • Debrabant , K. , and Kværn⊘ , A. 2008–2009 . B-series analysis of stochastic Runge–Kutta methods that use an iterative scheme to compute their internal stage values . SIAM Journal on Numerical Analysis 47 ( 1 ): 181 – 203 .
  • Kloeden , P.E. , and Platen , E. 1991 . Relations between multiple It⊚ and Stratonovich integrals . Stochastic Analysis and Applications 9 ( 3 ): 311 – 321 .
  • Kloeden , P.E. , and Platen , E. 1991 . Stratonovich and Itô stochastic Taylor expansions . Mathematische Nachrichten 151 : 33 – 50 .
  • Kloeden , P.E. , and Platen , E. 1999 . Numerical Solution of Stochastic Differential Equations: Vol. 21 Applications of Mathematics. , 2 ed. Springer-Verlag , Berlin .
  • Komori , Y. , Mitsui , T. , and Sugiura , H. 1997 . Rooted tree analysis of the order conditions of ROW-type scheme for stochastic differential equations . BIT 37 ( 1 ): 43 – 66 .
  • Rößler , A. 2004 . Stochastic Taylor expansions for the expectation of functionals of diffusion processes . Stochastic Analysis and Applications 22 ( 6 ): 1553 – 1576 .
  • Rößler , A. 2006 . Rooted tree analysis for order conditions of stochastic Runge–Kutta methods for the weak approximation of stochastic differential equations . Stochastic Analysis and Applications 24 ( 1 ): 97 – 134 .

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