Numerical approximation for a white noise driven SPDE with locally bounded drift

Potential Analysis

Volumn 22, Issue 4, 2005, Pages 375-393

  Pettersson, Roger ^a   Signahl, Mikael ^b  

^a LINNAEUS UNIVERSITY   (Sweden)

^b LUND UNIVERSITY   (Sweden)

Author keywords

Malliavin calculus; Stochastic partial differential equations

Indexed keywords

EID: 15444363340     PISSN: 09262601     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11118-004-1329-4     Document Type: Article

References (21)

1. Allen, E.J., Novosel, S.J. and Zhang, Z.: 'Finite element and difference approximation of some linear stochastic partial differential equations', Stoch. Stoch. Rep. 64 (1998), 117-142.
2. Bass, R.F.: Diffusions and Elliptic Operators, Springer, Berlin, 1997.
3. Bally, V., Gyöngy, I. and Pardoux, E.: 'White noise driven parabolic SPDEs with measurable drift', J. Funct. Anal. 120 (1994), 484-510.
4. Billingsley, P.: Convergence of Probability Measures, Wiley, New York, 1968.
5. Davie, A.M. and Gaines, J.G.: 'Convergence of numerical schemes for the solution of parabolic stochastic partial differential equations', Math. Comp. 70(233) (2000), 121-134.
6. Funaki, T.: 'Random motion of strings and related evolution equations', Nagoya Math. J. 89 (1983), 129-193.
7. Gyöngy, I.: 'On non-degenerate quasi-linear stochastic partial differential equations', Pot. Anal. 4(1995), 157-171.
8. Gyöngy, I.: 'Lattice approximations for stochastic quasi-linear parabolic partial differential equations driven by space-time white noise II', Pot. Anal. 11 (1999), 1-37.
9. Gyöngy, I. and Krylov, N.: 'Existence of strong solutions for Itô's stochastic equations via approximations', Probab. Theory Related Fields 105(2) (1996), 143-158.
10. Gyöngy, I. and Nualart, D.: 'Implicit scheme for stochastic parabolic partial differential equations driven by space-time white noise', Pot. Anal. 7 (1997), 725-757.
11. Gyöngy, I. and Pardoux, E.: On quasi-linear stochastic partial differential equations', Probab. Theory Related Fields 94 (1993), 413-425.
12. Gyöngy, I. and Pardoux, E.: 'On the regularization effect of space-time white noise on quasi-linear parabolic partial differential equations', Probab. Theory Related Fields 97 (1993), 211-229.
13. Ikeda, N. and Watanabe, S.: Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam, 1989.
14. Janson, S.: Gaussian Hilbert Spaces, Cambridge Univ. Press, Cambridge, 1997.
15. Malliavin, P.: Stochastic Analysis, Springer, Berlin, 1997.
16. Nualart, D.: 'Analysis on Wiener space and anticipating calculus', in Lecture Notes in Mathematics 1690, Springer, New York, 1998, pp. 123-227.
17. Nualart, D.: The Malliavin Calculus and Related Topics, Springer, Berlin, 1995.
18. Skorokhod, A.V.: Studies in the Theory of Random Processes, Addison-Wesley, Reading, MA, 1965.
19. Shardlow, T.: 'Numerical methods for stochastic parabolic PDE's', Numer. Funct. Anal. Optim. 20 (1999), 121-145.
20. Üstünel, A.S.: An Introduction to Analysis on Wiener Space, Lecture Notes in Mathematics 1610, Springer, New York, 1995.
21. Walsh, J.: An Introduction to Stochastic Partial Differential Equations, Lecture Notes in Mathematics 1180, Springer, New York, 1986.