메뉴 건너뛰기




Volumn 206, Issue 1, 2007, Pages 158-173

Weak second-order stochastic Runge-Kutta methods for non-commutative stochastic differential equations

Author keywords

Derivative free; Explicit scheme; Multi colored rooted tree; Multi dimensional Wiener process; Multiplicative noise

Indexed keywords

NUMERICAL METHODS; RANDOM VARIABLES; RUNGE KUTTA METHODS; STOCHASTIC CONTROL SYSTEMS;

EID: 34249278816     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2006.06.006     Document Type: Article
Times cited : (33)

References (18)
  • 1
    • 0032182723 scopus 로고    scopus 로고
    • General order conditions for stochastic Runge-Kutta methods for both commuting and non-commuting stochastic ordinary differential equation systems
    • Burrage K., and Burrage P.M. General order conditions for stochastic Runge-Kutta methods for both commuting and non-commuting stochastic ordinary differential equation systems. Appl. Numer. Math. 28 (1998) 161-177
    • (1998) Appl. Numer. Math. , vol.28 , pp. 161-177
    • Burrage, K.1    Burrage, P.M.2
  • 2
    • 0034547253 scopus 로고    scopus 로고
    • Order conditions of stochastic Runge-Kutta methods by B-series
    • Burrage K., and Burrage P.M. Order conditions of stochastic Runge-Kutta methods by B-series. SIAM J. Numer. Anal. 38 5 (2000) 1626-1646
    • (2000) SIAM J. Numer. Anal. , vol.38 , Issue.5 , pp. 1626-1646
    • Burrage, K.1    Burrage, P.M.2
  • 3
    • 1542512456 scopus 로고    scopus 로고
    • Numerical methods for strong solutions of stochastic differential equations: an overview
    • Burrage K., Burrage P.M., and Tian T. Numerical methods for strong solutions of stochastic differential equations: an overview. Proc. Roy. Soc. London A 460 (2004) 373-402
    • (2004) Proc. Roy. Soc. London A , vol.460 , pp. 373-402
    • Burrage, K.1    Burrage, P.M.2    Tian, T.3
  • 5
    • 0001512119 scopus 로고
    • Inversive congruential pseudorandom numbers: a tutorial
    • Eichenauer-Herrmann J. Inversive congruential pseudorandom numbers: a tutorial. Internat. Statist. Rev. 60 2 (1992) 167-176
    • (1992) Internat. Statist. Rev. , vol.60 , Issue.2 , pp. 167-176
    • Eichenauer-Herrmann, J.1
  • 7
    • 34249301902 scopus 로고    scopus 로고
    • P.E. Kloeden, E. Platen, Numerical Solution of Stochastic Differential Equations, Corrected 3rd printing, Springer, New York, 1999.
  • 8
    • 33846257307 scopus 로고    scopus 로고
    • Y. Komori, Multi-colored rooted tree analysis of the weak order conditions of a stochastic Runge-Kutta family, Appl. Numer. Math., in press, doi: 10.1016/j.apnum.2006.02.002.
  • 9
    • 33847361411 scopus 로고    scopus 로고
    • Y. Komori, Weak order stochastic Runge-Kutta methods for commutative stochastic differential equations, J. Comput. Appl. Math., in press, doi: 10.1016/j.cam.2006.03.010.
  • 10
    • 0005272542 scopus 로고
    • Stable ROW-type weak scheme for stochastic differential equations
    • Komori Y., and Mitsui T. Stable ROW-type weak scheme for stochastic differential equations. Monte Carlo Methods Appl. 1 4 (1995) 279-300
    • (1995) Monte Carlo Methods Appl. , vol.1 , Issue.4 , pp. 279-300
    • Komori, Y.1    Mitsui, T.2
  • 11
    • 0000082822 scopus 로고
    • Some issue in discrete approximate solution for stochastic differential equations
    • Komori Y., Saito Y., and Mitsui T. Some issue in discrete approximate solution for stochastic differential equations. Comput. Math. Appl. 28 10-12 (1994) 269-278
    • (1994) Comput. Math. Appl. , vol.28 , Issue.10-12 , pp. 269-278
    • Komori, Y.1    Saito, Y.2    Mitsui, T.3
  • 12
    • 84972042314 scopus 로고
    • Higher-order weak approximation of Ito diffusions by Markov chains
    • Platen E. Higher-order weak approximation of Ito diffusions by Markov chains. Probab. Eng. Inform. Sci. 6 (1992) 391-408
    • (1992) Probab. Eng. Inform. Sci. , vol.6 , pp. 391-408
    • Platen, E.1
  • 13
    • 34249336914 scopus 로고    scopus 로고
    • A. Rößler, Runge-Kutta methods for the numerical solution of stochastic differential equations, Ph.D. Thesis, Darmstadt University of Technology, Germany, 2003.
  • 14
    • 1442264991 scopus 로고    scopus 로고
    • Runge-Kutta methods for Stratonovich stochastic differential equation systems with commutative noise
    • Rößler A. Runge-Kutta methods for Stratonovich stochastic differential equation systems with commutative noise. J. Comput. Appl. Math. 164-165 (2004) 613-627
    • (2004) J. Comput. Appl. Math. , vol.164-165 , pp. 613-627
    • Rößler, A.1
  • 15
    • 30444461217 scopus 로고    scopus 로고
    • Rooted tree analysis for order conditions of stochastic Runge-Kutta methods for the weak approximation of stochastic differential equations
    • Rößler A. Rooted tree analysis for order conditions of stochastic Runge-Kutta methods for the weak approximation of stochastic differential equations. Stochastic Anal. Appl. 24 1 (2006) 97-134
    • (2006) Stochastic Anal. Appl. , vol.24 , Issue.1 , pp. 97-134
    • Rößler, A.1
  • 16
    • 34249304988 scopus 로고    scopus 로고
    • D. Talay, Simulation of stochastic differential systems, Probab. Methods Appl. Phys. (1995) 54-96.
  • 17
    • 0000124397 scopus 로고
    • Expansion of the global error for numerical schemes solving stochastic differential equations
    • Talay D., and Tubaro L. Expansion of the global error for numerical schemes solving stochastic differential equations. Stochastic Anal. Appl. 8 4 (1990) 483-509
    • (1990) Stochastic Anal. Appl. , vol.8 , Issue.4 , pp. 483-509
    • Talay, D.1    Tubaro, L.2
  • 18
    • 0037246360 scopus 로고    scopus 로고
    • Weak second order conditions for stochastic Runge-Kutta methods
    • Tocino A., and Vigo-Aguiar J. Weak second order conditions for stochastic Runge-Kutta methods. SIAM J. Sci. Comput. 24 2 (2002) 507-523
    • (2002) SIAM J. Sci. Comput. , vol.24 , Issue.2 , pp. 507-523
    • Tocino, A.1    Vigo-Aguiar, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.