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Volumn 47, Issue 2, 2007, Pages 393-418

An implicit Euler scheme with non-uniform time discretization for heat equations with multiplicative noise

Author keywords

Implicit Euler scheme; Multiplicative noise; Non uniform time discretization; Optimality; Rate of convergence; Stochastic heat equation

Indexed keywords


EID: 34250880991     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10543-007-0129-9     Document Type: Article
Times cited : (33)

References (17)
  • 2
    • 0007470214 scopus 로고    scopus 로고
    • Exact convergence rate of the Euler-Maruyama scheme, with application to sampling design
    • S. Cambanis and Y. Hu, Exact convergence rate of the Euler-Maruyama scheme, with application to sampling design, Stochastics Stochastics Rep., 59 (1996), pp. 211-240.
    • (1996) Stochastics Stochastics Rep , vol.59 , pp. 211-240
    • Cambanis, S.1    Hu, Y.2
  • 4
    • 0035605884 scopus 로고    scopus 로고
    • Convergence of numerical schemes for the solution of parabolic partial differential equations
    • A. M. Davie and J. Gaines, Convergence of numerical schemes for the solution of parabolic partial differential equations, Math. Comput., 70 (2001), pp. 121-134.
    • (2001) Math. Comput , vol.70 , pp. 121-134
    • Davie, A.M.1    Gaines, J.2
  • 5
    • 0042078403 scopus 로고    scopus 로고
    • Lattice approximations for stochastic quasi-linear parabolic partial differential equations driven by space-time white noise II
    • I. Gyöngy, Lattice approximations for stochastic quasi-linear parabolic partial differential equations driven by space-time white noise II, Potential Anal., 11 (1999), pp. 1-37.
    • (1999) Potential Anal , vol.11 , pp. 1-37
    • Gyöngy, I.1
  • 6
    • 0037107474 scopus 로고    scopus 로고
    • Numerical analysis of semilinear stochastic evolution equations in Banach spaces
    • E. Hausenblas, Numerical analysis of semilinear stochastic evolution equations in Banach spaces, J. Comput. Appl. Math., 147 (2002), pp. 485-516.
    • (2002) J. Comput. Appl. Math , vol.147 , pp. 485-516
    • Hausenblas, E.1
  • 7
    • 0037209607 scopus 로고    scopus 로고
    • Approximation for semilinear stochastic evolution equations
    • E. Hausenblas, Approximation for semilinear stochastic evolution equations, Potential Anal., 18 (2003), pp. 141-186.
    • (2003) Potential Anal , vol.18 , pp. 141-186
    • Hausenblas, E.1
  • 8
    • 0035294723 scopus 로고    scopus 로고
    • The optimal discretization of stochastic differential equations
    • N. Hofmann, T. Müller-Gronbach, and K. Ritter, The optimal discretization of stochastic differential equations, J. Complexity, 17 (2001), pp. 117-153.
    • (2001) J. Complexity , vol.17 , pp. 117-153
    • Hofmann, N.1    Müller-Gronbach, T.2    Ritter, K.3
  • 9
    • 0012150629 scopus 로고    scopus 로고
    • Linear-implicit strong schemes for Itô-Galerkin approximations of stochastic PDEs
    • P. Kloeden and S. Shott, Linear-implicit strong schemes for Itô-Galerkin approximations of stochastic PDEs, J. Appl. Math. Stochastic Anal., 14 (2001), pp. 47-53.
    • (2001) J. Appl. Math. Stochastic Anal , vol.14 , pp. 47-53
    • Kloeden, P.1    Shott, S.2
  • 11
    • 0041969994 scopus 로고    scopus 로고
    • Optimal uniform approximation of systems of stochastic differential equations
    • T. Müller-Gronbach, Optimal uniform approximation of systems of stochastic differential equations, Ann. Appl. Probab., 12 (2002), pp. 664-690.
    • (2002) Ann. Appl. Probab , vol.12 , pp. 664-690
    • Müller-Gronbach, T.1
  • 12
    • 26844485169 scopus 로고    scopus 로고
    • Optimal pointwise approximation of SDEs based on Brownian motion at discrete points
    • T. Müller-Gronbach, Optimal pointwise approximation of SDEs based on Brownian motion at discrete points, Ann. Appl. Probab., 14 (2004), pp. 1605-1642.
    • (2004) Ann. Appl. Probab , vol.14 , pp. 1605-1642
    • Müller-Gronbach, T.1
  • 13
    • 34250182382 scopus 로고    scopus 로고
    • Lower bounds and nonuniform time discretization for approximation of stochastic heat equations, to appear in Found. Comput. Math
    • T. Müller-Gronbach and K. Ritter, Lower bounds and nonuniform time discretization for approximation of stochastic heat equations, to appear in Found. Comput. Math., (2007), online first: http://dx.doi.org/10.1007/ s10208-005-0166-6.
    • (2007) online first
    • Müller-Gronbach, T.1    Ritter, K.2
  • 15
    • 20344379438 scopus 로고    scopus 로고
    • On implicit and explicit discretization schemes for parabolic SPDEs in any dimension
    • A. Millet and P.-L. Morien, On implicit and explicit discretization schemes for parabolic SPDEs in any dimension, Stochastic Processes Appl., 115 (2005), pp. 1073-1106.
    • (2005) Stochastic Processes Appl , vol.115 , pp. 1073-1106
    • Millet, A.1    Morien, P.-L.2
  • 16
    • 21244455730 scopus 로고    scopus 로고
    • Finite element methods for parabolic stochastic PDE's
    • J. B. Walsh, Finite element methods for parabolic stochastic PDE's, Potential Anal., 23 (2005), pp. 1-43.
    • (2005) Potential Anal , vol.23 , pp. 1-43
    • Walsh, J.B.1
  • 17
    • 33747184742 scopus 로고    scopus 로고
    • Galerkin finite element methods for stochastic parabolic partial differential equations
    • Y. Yan, Galerkin finite element methods for stochastic parabolic partial differential equations, SIAM J. Numer. Anal, 43 (2005), pp. 1363-1384.
    • (2005) SIAM J. Numer. Anal , vol.43 , pp. 1363-1384
    • Yan, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.