메뉴 건너뛰기




Volumn 44, Issue 2, 2006, Pages 779-803

Multistep methods for SDES and their application to problems with small noise

Author keywords

Mean square consistency; Mean square convergence; Mean square numerical stability; Small noise; Stochastic linear multistep method; Two step Maruyama methods

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; PARAMETER ESTIMATION; PROBLEM SOLVING; STOCHASTIC MODELS;

EID: 33646386596     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/040602857     Document Type: Article
Times cited : (74)

References (31)
  • 1
    • 0012329392 scopus 로고    scopus 로고
    • Numerical analysis of explicit one-step methods for stochastic delay differential equations
    • C. BAKER AND E. BUCKWAR, Numerical analysis of explicit one-step methods for stochastic delay differential equations, LMS J. Comput. Math., 3 (2000), pp. 315-335.
    • (2000) LMS J. Comput. Math , vol.3 , pp. 315-335
    • BAKER, C.1    BUCKWAR, E.2
  • 2
    • 3142555960 scopus 로고    scopus 로고
    • On two-step methods for stochastic differential equations
    • R. H. BOKOR, On two-step methods for stochastic differential equations, Acta Cybernet., 13 (1997), pp. 197-207.
    • (1997) Acta Cybernet , vol.13 , pp. 197-207
    • BOKOR, R.H.1
  • 4
    • 0037297001 scopus 로고    scopus 로고
    • Stochastically stable one-step approximations of solutions of stochastic ordinary differential equations, 3
    • R. H. BOKOR, Stochastically stable one-step approximations of solutions of stochastic ordinary differential equations, 3. Appl. Numer. Math., 44 (2003), pp. 299-312.
    • (2003) Appl. Numer. Math , vol.44 , pp. 299-312
    • BOKOR, R.H.1
  • 5
    • 0042185152 scopus 로고    scopus 로고
    • Adams-type methods for the numerical solution of stochastic ordinary differential equations
    • L. BRUGNANO, K. BURRAGE, AND P. BURRAGE, Adams-type methods for the numerical solution of stochastic ordinary differential equations, BIT, 40 (2000), pp. 451-470.
    • (2000) BIT , vol.40 , pp. 451-470
    • BRUGNANO, L.1    BURRAGE, K.2    BURRAGE, P.3
  • 6
    • 34247187113 scopus 로고    scopus 로고
    • On two-step schemes for SDEs with small noise
    • E. BUCKWAR AND R. WINKLER, On two-step schemes for SDEs with small noise, PAMM, 4 (2004), pp. 16-18.
    • (2004) PAMM , vol.4 , pp. 16-18
    • BUCKWAR, E.1    WINKLER, R.2
  • 7
    • 34248208111 scopus 로고    scopus 로고
    • Improved linear multi-step methods for stochastic ordinary differential equations
    • to appear
    • E. BUCKWAR AND R. WINKLER, Improved linear multi-step methods for stochastic ordinary differential equations, J. Comput. Appl. Math., to appear.
    • J. Comput. Appl. Math
    • BUCKWAR, E.1    WINKLER, R.2
  • 8
    • 0032182723 scopus 로고    scopus 로고
    • General order conditions for stochastic Runge-Kutta methods for both commuting and non-commuting stochastic ordinary differential equation systems
    • K. BURRAGE AND P. M. BURRAGE, General order conditions for stochastic Runge-Kutta methods for both commuting and non-commuting stochastic ordinary differential equation systems., Appl. Numer. Math., 28 (1998), pp. 161-177.
    • (1998) Appl. Numer. Math , vol.28 , pp. 161-177
    • BURRAGE, K.1    BURRAGE, P.M.2
  • 10
    • 0021852361 scopus 로고
    • 33 years of numerical instability, Part I
    • G. DAHLQUIST, 33 years of numerical instability, Part I, BIT, 25 (1985), pp. 188-204.
    • (1985) BIT , vol.25 , pp. 188-204
    • DAHLQUIST, G.1
  • 11
    • 0031359307 scopus 로고    scopus 로고
    • Adams methods for the efficient solution of stochastic differential equations with additive noise
    • G. DENK AND S. SCHÄPPLER, Adams methods for the efficient solution of stochastic differential equations with additive noise, Computing, 59 (1996), pp. 153-161.
    • (1996) Computing , vol.59 , pp. 153-161
    • DENK, G.1    SCHÄPPLER, S.2
  • 12
    • 34247267365 scopus 로고    scopus 로고
    • Modeling and simulation of transient noise in circuit simulation
    • to appear
    • G. DENK AND R. WINKLER, Modeling and simulation of transient noise in circuit simulation, Math. Comput. Modelling, to appear.
    • Math. Comput. Modelling
    • DENK, G.1    WINKLER, R.2
  • 13
    • 29144534675 scopus 로고    scopus 로고
    • Numerical analysis of stochastic schemes in geophysics
    • B. D. EWALD AND R. TÉMAM, Numerical analysis of stochastic schemes in geophysics, SIAM J. Numer. Anal., 42 (2005), pp. 2257-2276.
    • (2005) SIAM J. Numer. Anal , vol.42 , pp. 2257-2276
    • EWALD, B.D.1    TÉMAM, R.2
  • 16
    • 0004317158 scopus 로고
    • Solving Ordinary Differential Equations. 1: Nonstiff Problems
    • 2nd rev. ed, Springer, New York
    • E. HAIRER, S. P. NØRSETT, AND G. WANNER, Solving Ordinary Differential Equations. 1: Nonstiff Problems, 2nd rev. ed., Springer Ser. Comput. Math. 8, Springer, New York, 1993.
    • (1993) Springer Ser. Comput. Math , vol.8
    • HAIRER, E.1    NØRSETT, S.P.2    WANNER, G.3
  • 20
    • 84980086027 scopus 로고
    • Survey of the stability of linear finite difference equations
    • P. LAX AND R. RICHTMYER, Survey of the stability of linear finite difference equations, Comm. Pure Appl. Math., 9 (1956), pp. 267-293.
    • (1956) Comm. Pure Appl. Math , vol.9 , pp. 267-293
    • LAX, P.1    RICHTMYER, R.2
  • 21
    • 0031173522 scopus 로고    scopus 로고
    • Mean-square numerical methods for stochastic differential equations with small noise
    • G. MILSTEIN AND M. TRETYAKOV, Mean-square numerical methods for stochastic differential equations with small noise, SIAM J. Sci. Comput., 18 (1997), pp. 1067-1087.
    • (1997) SIAM J. Sci. Comput , vol.18 , pp. 1067-1087
    • MILSTEIN, G.1    TRETYAKOV, M.2
  • 23
    • 0012439159 scopus 로고
    • Theorem on the order of convergence for mean-square approximations of solutions of stochastic differential equations
    • G. MILSTEIN, Theorem on the order of convergence for mean-square approximations of solutions of stochastic differential equations, Theory Probab. Appl., 32 (1987), pp. 738-741.
    • (1987) Theory Probab. Appl , vol.32 , pp. 738-741
    • MILSTEIN, G.1
  • 25
    • 0034159721 scopus 로고    scopus 로고
    • A new numerical method for sdes and its application in circuit simulation, 3
    • C. PENSKI, A new numerical method for sdes and its application in circuit simulation, 3. Comput. Appl. Math., 115 (2000), pp. 461-470.
    • (2000) Comput. Appl. Math , vol.115 , pp. 461-470
    • PENSKI, C.1
  • 27
    • 34247189849 scopus 로고    scopus 로고
    • W. RÖMISCH AND R. WINKLER, Stochastic DAEs in circuit simulation, in Modeling, Simulation and Optimization of Integrated Circuits, A. G. K. Antreich, R. Bulirsch and P. Rentrop, eds., Birkhäuser, Basel, Switzerland, 2003, pp. 303-318.
    • W. RÖMISCH AND R. WINKLER, Stochastic DAEs in circuit simulation, in Modeling, Simulation and Optimization of Integrated Circuits, A. G. K. Antreich, R. Bulirsch and P. Rentrop, eds., Birkhäuser, Basel, Switzerland, 2003, pp. 303-318.
  • 28
    • 0007336796 scopus 로고    scopus 로고
    • On the simulation of iterated Itô integrals
    • T. RYDÉN AND M. WIKTORSSON, On the simulation of iterated Itô integrals, Stochastic Process. Appl., 91 (2001), pp. 151-168.
    • (2001) Stochastic Process. Appl , vol.91 , pp. 151-168
    • RYDÉN, T.1    WIKTORSSON, M.2
  • 29
    • 0035538464 scopus 로고    scopus 로고
    • Joint characteristic function and simultaneous simulation of iterated Itô integrals for multiple independent Brownian motions
    • M. WIKTORSSON, Joint characteristic function and simultaneous simulation of iterated Itô integrals for multiple independent Brownian motions, Ann. Appl. Probab., 11 (2001), pp. 470-487.
    • (2001) Ann. Appl. Probab , vol.11 , pp. 470-487
    • WIKTORSSON, M.1
  • 30
    • 0041519194 scopus 로고    scopus 로고
    • Stochastic differential algebraic equations of index 1 and applications in circuit simulation
    • R. WINKLER, Stochastic differential algebraic equations of index 1 and applications in circuit simulation, J. Comput. Appl. Math., 157 (2003), pp. 477-505.
    • (2003) J. Comput. Appl. Math , vol.157 , pp. 477-505
    • WINKLER, R.1
  • 31
    • 85048546414 scopus 로고    scopus 로고
    • Stochastic DAEs in transient noise simulation
    • Proceedings of Scientific Computing in Electrical Engineering, Springer, Berlin
    • R. WINKLER, Stochastic DAEs in transient noise simulation, in Proceedings of Scientific Computing in Electrical Engineering, Eindhoven Springer Series Mathematics in Industry, Springer, Berlin, 2004, pp. 408-415.
    • (2004) Eindhoven Springer Series Mathematics in Industry , pp. 408-415
    • WINKLER, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.