메뉴 건너뛰기




Volumn 33, Issue 6, 1996, Pages 2254-2267

Stability analysis of numerical schemes for Stochastic differential equations

Author keywords

Numerical schemes; Numerical stability; Stochastic differential equations

Indexed keywords


EID: 0000007761     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142992228409     Document Type: Article
Times cited : (307)

References (24)
  • 1
    • 1542532769 scopus 로고
    • Certain aspects of application of numerical methods for solving SDE systems
    • S. S. ARTEMIEV, Certain aspects of application of numerical methods for solving SDE systems, Bull. Nov. Comput. Center, Numer. Anal., 1(1993), pp. 1-16.
    • (1993) Bull. Nov. Comput. Center, Numer. Anal. , vol.1 , pp. 1-16
    • Artemiev, S.S.1
  • 4
    • 0008091778 scopus 로고
    • A-stability of Runge-Kutta Methods for systems with additive noise
    • D. B. HERNANDEZ AND R. SPIGLER, A-stability of Runge-Kutta Methods for systems with additive noise, BIT, 32(1992), pp. 620-633.
    • (1992) BIT , vol.32 , pp. 620-633
    • Hernandez, D.B.1    Spigler, R.2
  • 5
    • 0022388467 scopus 로고
    • Numerical integration of multiplicative-noise stochastic differential equations
    • J. R. KLAUDER AND W. P. PETERSEN, Numerical integration of multiplicative-noise stochastic differential equations, SIAM J. Numer. Anal., 22(1985), pp. 1153-1166.
    • (1985) SIAM J. Numer. Anal. , vol.22 , pp. 1153-1166
    • Klauder, J.R.1    Petersen, W.P.2
  • 6
    • 0024807350 scopus 로고
    • A survey of numerical methods for stochastic differential equations
    • P. E. KLOEDEN AND E. PLATEN, A survey of numerical methods for stochastic differential equations, J. Stoch. Hydrol. Hydraulics, 3(1989), pp. 155-178.
    • (1989) J. Stoch. Hydrol. Hydraulics , vol.3 , pp. 155-178
    • Kloeden, P.E.1    Platen, E.2
  • 8
    • 0000204594 scopus 로고
    • Higher order implicit strong numerical schemes for stochastic differential equations
    • _, Higher order implicit strong numerical schemes for stochastic differential equations, J. Statist. Phys., 66(1992), pp. 283-314.
    • (1992) J. Statist. Phys. , vol.66 , pp. 283-314
  • 9
    • 0041012325 scopus 로고
    • The numerical solution of nonlinear stochastic dynamical systems: A brief introduction
    • P. E. KLOEDEN, E. PLATEN, AND H, SCHURZ, The numerical solution of nonlinear stochastic dynamical systems: A brief introduction, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 1(1991), pp. 277-286.
    • (1991) Internat. J. Bifur. Chaos Appl. Sci. Engrg. , vol.1 , pp. 277-286
    • Kloeden, P.E.1    Platen, E.2    Schurz, H.3
  • 10
    • 64849113583 scopus 로고
    • Generalized cumulant expansion method
    • R. KUBO, Generalized cumulant expansion method, J. Phys. Soc. Japan, 17(1962), pp. 1100-1120.
    • (1962) J. Phys. Soc. Japan , vol.17 , pp. 1100-1120
    • Kubo, R.1
  • 12
    • 0023385089 scopus 로고
    • Simulation studies on time discrete diffusion approximations
    • H. LISKE AND E. PLATEN, Simulation studies on time discrete diffusion approximations, Math. Comput. Simulation, 29(1987), pp. 253-260.
    • (1987) Math. Comput. Simulation , vol.29 , pp. 253-260
    • Liske, H.1    Platen, E.2
  • 13
    • 0003074014 scopus 로고
    • Continuous Markov processes and stochastic equations
    • G. MARUYAMA, Continuous Markov processes and stochastic equations, Rend. Circ. Mat. Palermo, 4(1955), pp. 48-90.
    • (1955) Rend. Circ. Mat. Palermo , vol.4 , pp. 48-90
    • Maruyama, G.1
  • 15
    • 0000532550 scopus 로고
    • Approximate integration of stochastic differential equations
    • G. N. MIL'SHTEIN, Approximate integration of stochastic differential equations, Theory Probab. Appl., 19(1974), pp. 557-562.
    • (1974) Theory Probab. Appl. , vol.19 , pp. 557-562
    • Mil'shtein, G.N.1
  • 16
    • 0026138294 scopus 로고
    • Asymptotically efficient Runge-Kutta methods for a class of Ito and Stratonovich equations
    • N. J. NEWTON, Asymptotically efficient Runge-Kutta methods for a class of Ito and Stratonovich equations, SIAM J. Appl. Math., 51(1991), pp. 542-567.
    • (1991) SIAM J. Appl. Math. , vol.51 , pp. 542-567
    • Newton, N.J.1
  • 17
    • 0002004221 scopus 로고
    • Numerical simulation of Ito stochastic differential equations on supercomputers
    • W. P. PETERSEN, Numerical simulation of Ito stochastic differential equations on supercomputers, in Random Media, Springer IMA Series, 7(1987), pp. 215-228.
    • (1987) Random Media, Springer IMA Series , vol.7 , pp. 215-228
    • Petersen, W.P.1
  • 18
    • 0002503075 scopus 로고
    • Discretization and simulation of stochastic differential equations
    • E. PARDOUX AND D. TALAY, Discretization and simulation of stochastic differential equations, Acta Appl. Math., 3(1985), pp. 23-47.
    • (1985) Acta Appl. Math. , vol.3 , pp. 23-47
    • Pardoux, E.1    Talay, D.2
  • 19
    • 0002151247 scopus 로고
    • An approximation method for a class of Ito processes
    • E. PLATEN, An approximation method for a class of Ito processes, Lithuanian Math. J., 21(1981), pp. 121-133.
    • (1981) Lithuanian Math. J. , vol.21 , pp. 121-133
    • Platen, E.1
  • 20
    • 0001040012 scopus 로고
    • Numerical treatment of stochastic differential equations
    • W. RÜMELIN, Numerical treatment of stochastic differential equations, SIAM J. Numer. Anal., 19(1982), pp. 604-613.
    • (1982) SIAM J. Numer. Anal. , vol.19 , pp. 604-613
    • Rümelin, W.1
  • 21
    • 1542532766 scopus 로고
    • Discrete approximations for stochastic differential equations
    • in Japanese
    • Y. SAITO AND T. MITSUI, Discrete approximations for stochastic differential equations, Trans. Japan SIAM, 2(1992), pp. 1-16 (in Japanese).
    • (1992) Trans. Japan SIAM , vol.2 , pp. 1-16
    • Saito, Y.1    Mitsui, T.2
  • 22
    • 0003052614 scopus 로고
    • T-stability of numerical scheme for stochastic differential equations
    • _, T-stability of numerical scheme for stochastic differential equations, World Sci. Ser. Appl. Anal., 2(1993), pp. 333-344.
    • (1993) World Sci. Ser. Appl. Anal. , vol.2 , pp. 333-344
  • 23
    • 0009576144 scopus 로고
    • Simulation of stochastic differential equations
    • _, Simulation of stochastic differential equations, Ann. Inst. Statist. Math., 45(1993), pp. 419-432.
    • (1993) Ann. Inst. Statist. Math. , vol.45 , pp. 419-432
  • 24
    • 0026202362 scopus 로고
    • Approximation of upper Lyapunov exponents of bilinear stochastic differential systems
    • D. TALAY, Approximation of upper Lyapunov exponents of bilinear stochastic differential systems, SIAM J. Numer. Anal., 28 (1991), pp. 1141-1164.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 1141-1164
    • Talay, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.