REFERENCES
- Burrage , K. , and P. M. Burrage . 1996 . High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations . Appl. Numer. Math. 22 ( 1–3 ): 81 – 101 . [CSA]
- Burrage , K. , and P. M. Burrage . 2000 . Order conditions of stochastic Runge-Kutta methods by B-series . SIAM J. Numer. Anal. 38 ( 5 ): 1626 – 1646 . [CSA] [CROSSREF]
- Butcher , J. C. 2003 . Numerical Methods for Ordinary Differential Equations . Chichester : John Wiley & Sons .
- Hairer , E. 1981 . Order conditions for numerical methods for partitioned ordinary differential equations . Numer. Math. 36 : 431 – 445 . [CSA] [CROSSREF]
- Hairer , E. , S. P. Nøtt , G. Wanner . 1993 . Solving Ordinary Differential Equations I . Berlin : Springer-Verlag .
- Karatzas , I. , and S. E. Shreve . 1999 . Brownian Motion and Stochastic Calculus . New York , Berlin : Springer .
- Kloeden , P. E. , and E. Platen . 1999 . Numerical Solution of Stochastic Differential Equations . Applications of Mathematics 23 . Berlin : Springer-Verlag .
- Komori , Y. , T. Mitsui , H. Sugiura . 1997 . Rooted tree analysis of the order conditions of ROW-type scheme for stochastic differential equations . BIT 37 ( 1 ): 43 – 66 . [CSA]
- Lehn , J. , A. Rößler , O. Schein . 2002 . Adaptive schemes for the numerical solution of SDEs – a comparison . J. Comput. Appl. Math. 138 ( 2 ): 297 – 308 . [CSA] [CROSSREF]
- Mackevicius , V. , and J. Navikas . 2001 . Second-order weak Runge-Kutta type methods for Itô equations . Math. Comput. Simul. 57 ( 1–2 ): 29 – 34 . [CSA] [CROSSREF]
- Milstein , G. N. , and M. V. Tretyakov . 2004 . Stochastic Numerics for Mathematical Physics . Berlin : Springer-Verlag .
- Milstein , G. N. 1995 . Numerical Integration of Stochastic Differential Equations . Dordrecht : Kluwer Academic Publishers .
- Milstein , G. N. 1986 . Weak approximation of solutions of systems of stochastic differential equations . Theory Probab. Appl. 30 : 750 – 766 . [CSA] [CROSSREF]
- Newton , N. J. 1991 . Asymptotically efficient Runge-Kutta methods for a class of Itô and Stratonovich equations . SIAM J. Appl. Math. 51 ( 2 ): 542 – 567 . [CSA] [CROSSREF]
- Rößler , A. 2003 . Embedded stochastic Runge-Kutta methods . Proc. Appl. Math. Mech. 2 ( 1 ): 461 – 462 . [CSA] [CROSSREF]
- Rößler , A. 2004 . Runge-Kutta methods for Stratonovich stochastic differential equation systems with commutative noise . J. Comput. Appl. Math. 164–165 : 613 – 627 . [CSA]
- Rößler , A. 2003 . Runge-Kutta Methods for the Numerical Solution of Stochastic Differential Equations , Ph.D. thesis , Darmstadt University of Technology .
- Rößler , A. 2004 . Stochastic Taylor expansions for the expectation of functionals of diffusion processes . Stochastic Anal. Appl. 22 ( 6 ): 1553 – 1576 . [CSA] [CROSSREF]
- Rümelin , W. 1982 . Numerical treatment of stochastic differential equations . SIAM J. Numer. Anal. 19 ( 3 ): 604 – 613 . [CSA] [CROSSREF]
- Talay , D. 1990 . Second-order discretization schemes of stochastic differential systems for the computation of the invariant law . Stochastics and Stochastic Rep. 29 ( 1 ): 13 – 36 . [CSA]
- Tocino , A. , and J. Vigo-Aguiar . 2002 . Weak second order conditions for stochastic Runge-Kutta methods . SIAM J. Sci. Comput. 24 ( 2 ): 507 – 523 . [CSA] [CROSSREF]