Weak convergence of a numerical method for a stochastic heat equation

BIT Numerical Mathematics

Volumn 43, Issue 1, 2003, Pages 179-193

  Shardlow, Tony ^a  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

Initial boundary value problems; Partial differential equations; Stochastic partial differential equations

Indexed keywords

EID: 4043178349     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1023661308243     Document Type: Article

References (14)

1. E. Buckwar and T. Shardlow, Weak approximation of stochastic delay differential equations, IMA J. Numer. Anal., submitted, 2001.
2. G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, Vol. 44 of Encyclopedia of Mathematics and its Applications, Cambridge University Press, Cambridge, 1992.
3. A. M. Davie and J. G. Gaines, Convergence of numerical schemes for the solution of parabolic stochastic partial differential equations, Math. Comp., 70 (2001), pp. 121-134.
4. W. Grecksch and P. Kloeden, Time-discretized Galerkin approximations of parabolic stochastic PDEs, Bull. Austral. Math. Soc., 54 (1996), pp. 79-85.
5. C. Gugg, Approximation of Stochastic PDEs and Turbulence in Fluids, PhD thesis, Augsburg, 2000.
6. I. Gyöngy, Lattice approximations for stochastic quasi-linear parabolic partial differential equations driven by space-time white noise I, Potential Anal., 19 (1998), pp. 1-25.
7. 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.
8. E. Hausenblas, Approximation for semilinear stochastic evolution equations, Potential Analysis, to appear.
9. P. E. Kloeden and E. Platen, Numerical solution of stochastic differential equations, Vol. 23 of Applications of Mathematics, Springer-Verlag, Berlin, 1992.
10. G. N. Milstein, The Numerical Integration of Stochastic Differential Equations, Kluwer Academic Publishers, Dordrecht, 1995.
11. J. Printems, On the discretization in time of parabolic stochastic partial differential equations, Monte Carlo Methods Appl., 7 (2001), pp. 359-368. Monte Carlo and probabilistic methods for partial differential equations, Part II (Monte Carlo, 2000).
12. J. Printems, On the discretization in time of parabolic stochastic partial differential equations, Monte Carlo Methods Appl., 7 (2001), pp. 359-368. Monte Carlo and probabilistic methods for partial differential equations, Part II (Monte Carlo, 2000).
13. T. Shardlow, Numerical methods for stochastic parabolic PDEs, Numer. Funct. Anal. Optim., 20 (1999), pp. 121-145. (The stability condition described here can be weakened to v(1 - 2θ) < 1/2.)
14. D. Talay, Efficient numerical schemes for the approximation of expectations of functionals of the solution of a SDE and applications, in Filtering and Control of Random Processes, J. Szpirglas, H. Korezlioglu, and G. Mazziotto, eds., Vol. 61, Lecture Notes in Control and Information Sciences, Springer-Verlag, Berlin, 1984, pp. 294-313.