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Volumn 24, Issue 4, 2006, Pages 303-332

Space semi-discretisations for a stochastic wave equation

Author keywords

Discretisation schemes; Stochastic partial differential equations; Wave equation

Indexed keywords


EID: 33745094134     PISSN: 09262601     EISSN: 1572929X     Source Type: Journal    
DOI: 10.1007/s11118-005-9002-0     Document Type: Article
Times cited : (59)

References (30)
  • 1
    • 33646561356 scopus 로고
    • Approximation of Zakai equation by the splitting-up method
    • (Warsaw 1988), Lecture Notes in Control and Inform. Sci. 136, Springer, Berlin
    • Bensoussan, A. and Glowinski, R.: 'Approximation of Zakai equation by the splitting-up method', in Stochastic Systems and Optimization, (Warsaw 1988), Lecture Notes in Control and Inform. Sci. 136, Springer, Berlin, 1989, pp. 257-265.
    • (1989) Stochastic Systems and Optimization , pp. 257-265
    • Bensoussan, A.1    Glowinski, R.2
  • 2
    • 0010032948 scopus 로고
    • Approximation of some stochastic differential equations by the splitting-up method
    • Bensoussan, A., Glowinski, R. and Rascanu, A.: 'Approximation of some stochastic differential equations by the splitting-up method', Appl. Math. Optim. 25(1) (1992), 81-106.
    • (1992) Appl. Math. Optim. , vol.25 , Issue.1 , pp. 81-106
    • Bensoussan, A.1    Glowinski, R.2    Rascanu, A.3
  • 4
    • 0007338853 scopus 로고
    • Random nonlinear wave equations: Smoothness of the solutions
    • Carmona, R. and Nualart, D.: 'Random nonlinear wave equations: Smoothness of the solutions', Probab. Theory Related Fields 79(4) (1988), 469-508.
    • (1988) Probab. Theory Related Fields , vol.79 , Issue.4 , pp. 469-508
    • Carmona, R.1    Nualart, D.2
  • 5
    • 0038620976 scopus 로고    scopus 로고
    • Numerical approximations of some linear stochastic partial differential equations driven by special additive noises
    • Du, Q. and Zhang, T.: 'Numerical approximations of some linear stochastic partial differential equations driven by special additive noises', SIAM J. Numer. Anal. 40(4) (2002), 1421-1445.
    • (2002) SIAM J. Numer. Anal. , vol.40 , Issue.4 , pp. 1421-1445
    • Du, Q.1    Zhang, T.2
  • 7
  • 8
    • 0003027298 scopus 로고    scopus 로고
    • Time-discretized Garlekin approximations of parabolic SPDEs
    • Grecksch, W. and Kloeden, P.E.: Time-discretized Garlekin approximations of parabolic SPDEs', Bull. Aust. Math. Soc. 54 (1996), 79-85.
    • (1996) Bull. Aust. Math. Soc. , vol.54 , pp. 79-85
    • Grecksch, W.1    Kloeden, P.E.2
  • 9
    • 0041725493 scopus 로고    scopus 로고
    • Lattice approximations for stochastic quasi-linear parabolic partial differential equations driven by space-time white noise I
    • Gyöngy, I.: 'Lattice approximations for stochastic quasi-linear parabolic partial differential equations driven by space-time white noise I', Potential Anal. 9(1) (1998), 1-25.
    • (1998) Potential Anal. , vol.9 , Issue.1 , pp. 1-25
    • Gyöngy, I.1
  • 10
    • 0042078403 scopus 로고    scopus 로고
    • Lattice approximations for stochastic quasi-linear parabolic partial differential equations driven by space-time white noise II
    • Gyöngy, I.: 'Lattice approximations for stochastic quasi-linear parabolic partial differential equations driven by space-time white noise II', Potential Anal. 11(1) (1999), 1-37.
    • (1999) Potential Anal. , vol.11 , Issue.1 , pp. 1-37
    • Gyöngy, I.1
  • 11
    • 4544297429 scopus 로고    scopus 로고
    • Approximations of stochastic partial differential equations
    • G. da Prato and L. Tubaro (eds), Lecture Notes in Pure and Appl. Math. 227, Marcel and Dekker
    • Gyöngy, I.: 'Approximations of stochastic partial differential equations', in G. da Prato and L. Tubaro (eds), Stochastic Partial Differential Equations and Applications, Lecture Notes in Pure and Appl. Math. 227, Marcel and Dekker, 2002, pp. 287-307.
    • (2002) Stochastic Partial Differential Equations and Applications , pp. 287-307
    • Gyöngy, I.1
  • 12
    • 18144433566 scopus 로고    scopus 로고
    • On the splitting-up method and stochastic partial differential equations
    • Gyöngy, I. and Krylov, N.: 'On the splitting-up method and stochastic partial differential equations', Ann. Probab. 31(2) (2003), 564-991.
    • (2003) Ann. Probab. , vol.31 , Issue.2 , pp. 564-991
    • Gyöngy, I.1    Krylov, N.2
  • 13
    • 33745077102 scopus 로고    scopus 로고
    • On the approximation of solutions of stochastic differential equations of elliptic type
    • to appear
    • Gyöngy, I. and Martínez, T.: 'On the approximation of solutions of stochastic differential equations of elliptic type', to appear in Stochastics and Stochastics Reports.
    • Stochastics and Stochastics Reports
    • Gyöngy, I.1    Martínez, T.2
  • 14
    • 17144406851 scopus 로고    scopus 로고
    • On discretization schemes for stochastic evolution equations
    • Gyöngy, I. and Millet, A.: 'On discretization schemes for stochastic evolution equations', Potential Anal. 23(2) (2005), 99-134.
    • (2005) Potential Anal. , vol.23 , Issue.2 , pp. 99-134
    • Gyöngy, I.1    Millet, A.2
  • 15
    • 4244153522 scopus 로고
    • Implicit scheme for quasi-linear parabolic partial differential equations perturbed by space-time white noise
    • Gyöngy, I. and Nualart, D.: 'Implicit scheme for quasi-linear parabolic partial differential equations perturbed by space-time white noise', Stochastic Process. Appl. 58(1) (1995), 57-72.
    • (1995) Stochastic Process. Appl. , vol.58 , Issue.1 , pp. 57-72
    • Gyöngy, I.1    Nualart, D.2
  • 16
    • 0042732714 scopus 로고    scopus 로고
    • Implicit scheme for stochastic parabolic partial differential equations driven by space-time white noise
    • Gyöngy, I. and Nualart, D.: 'Implicit scheme for stochastic parabolic partial differential equations driven by space-time white noise', Potential Anal. 7(4) (1997), 725-757.
    • (1997) Potential Anal. , vol.7 , Issue.4 , pp. 725-757
    • Gyöngy, I.1    Nualart, D.2
  • 17
    • 0037209607 scopus 로고    scopus 로고
    • Approximation for semi-linear stochastic evolution equations
    • Hausenblas, E.: 'Approximation for semi-linear stochastic evolution equations', Potential Anal. 18(2) (2003), 141-186.
    • (2003) Potential Anal. , vol.18 , Issue.2 , pp. 141-186
    • Hausenblas, E.1
  • 18
    • 0000889320 scopus 로고    scopus 로고
    • Approximation of the Kushner equation for nonlinear filtering
    • Itô, K. and Rozovskii, B.: 'Approximation of the Kushner equation for nonlinear filtering', SIAM J. Control Optim. 38 (2000), 893-915.
    • (2000) SIAM J. Control Optim. , vol.38 , pp. 893-915
    • Itô, K.1    Rozovskii, B.2
  • 22
    • 11144345650 scopus 로고    scopus 로고
    • Exact and fast numerical algorithms for the stochastic wave equation
    • Martin, A., Prigarin, S.M. and Winkler, G.: 'Exact and fast numerical algorithms for the stochastic wave equation', Int. J. Comput. Math. 80(12) (2003), 1535-1541.
    • (2003) Int. J. Comput. Math. , vol.80 , Issue.12 , pp. 1535-1541
    • Martin, A.1    Prigarin, S.M.2    Winkler, G.3
  • 23
    • 0033415166 scopus 로고    scopus 로고
    • A stochastic wave equation in two space dimension: Smoothness of the law
    • Millet, A. and Sanz-Solé, M.: 'A stochastic wave equation in two space dimension: Smoothness of the law', Ann. Probab. 27(2) (1999), 803-844.
    • (1999) Ann. Probab. , vol.27 , Issue.2 , pp. 803-844
    • Millet, A.1    Sanz-Solé, M.2
  • 24
    • 20344379438 scopus 로고    scopus 로고
    • On implicit and explicit discretization schemes for parabolic SPDEs in any dimension
    • Millet, A. and Morien, P.-L.: 'On implicit and explicit discretization schemes for parabolic SPDEs in any dimension', Stoc. Proc. Appl. 115(7) (2005), 1073-1106.
    • (2005) Stoc. Proc. Appl. , vol.115 , Issue.7 , pp. 1073-1106
    • Millet, A.1    Morien, P.-L.2
  • 25
    • 0035565493 scopus 로고    scopus 로고
    • On the discretization in time of parabolic stochastic partial differential equations
    • Printems, J.: 'On the discretization in time of parabolic stochastic partial differential equations', Math. Model. Numer. Anal. 35(6) (2001), 1055-1078.
    • (2001) Math. Model. Numer. Anal. , vol.35 , Issue.6 , pp. 1055-1078
    • Printems, J.1
  • 26
    • 0032676044 scopus 로고    scopus 로고
    • Numerical methods for stochastic parabolic PDEs
    • Shardlow, T.: 'Numerical methods for stochastic parabolic PDEs', Numer. Funct. Anal. Optim. 20 (1999), 121-145.
    • (1999) Numer. Funct. Anal. Optim. , vol.20 , pp. 121-145
    • Shardlow, T.1
  • 27
    • 4043178349 scopus 로고    scopus 로고
    • Weak convergence of a numerical method for a stochastic heat equation
    • Shardlow, T.: 'Weak convergence of a numerical method for a stochastic heat equation', BIT Numer. Math. 43 (2003), 179-193.
    • (2003) BIT Numer. Math. , vol.43 , pp. 179-193
    • Shardlow, T.1
  • 29
    • 0034395433 scopus 로고    scopus 로고
    • 1 by a finite difference method
    • 1 by a finite difference method', Math. Comput. 69 (2000), 653-666.
    • (2000) Math. Comput. , vol.69 , pp. 653-666
    • Yoo, H.1
  • 30
    • 0010586879 scopus 로고
    • (École d'été de Probabilités de Saint Flour XIV), Lecture Notes in Math. 1180, Springer, New York
    • Walsh, J.B.: An Introduction to Stochastic Partial Differential Equations, (École d'été de Probabilités de Saint Flour XIV), Lecture Notes in Math. 1180, Springer, New York, 1986.
    • (1986) An Introduction to Stochastic Partial Differential Equations
    • Walsh, J.B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.