Integration of stochastic differential equations on a computer

International Journal of Modern Physics C

Volumn 13, Issue 9, 2002, Pages 1177-1194

  Mannella, Riccardo ^a  

^a UNIVERSITY OF PISA   (Italy)

Author keywords

Correlated noise; Large fluctuations; Numerical integration; Stochastic differential equations

Indexed keywords

EID: 0036870950     PISSN: 01291831     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129183102004042     Document Type: Conference Paper

References (33)

1. D. G. Luchinsky, P. V. E. McClintock, and M. I. Dykman, Rep. Prog. Phys. 61, 889 (1998).
2. R. Mannella, in Noise in Nonlinear Dynamical Systems, III: Experiments and Simulations, eds. F. Moss and P. V. E. McClintock (CUP, Cambridge, 1989), pp. 189-221.
3. P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations (Springer-Verlag, Berlin, 1992).
4. R. Mannella, in Supercomputation in Nonlinear and Disordered Systems, eds. L. Vasquez, F. Tirado, and I. Martin (World Scientific, 1997), pp. 100-129.
5. J. Garcia-Ojalvo and J. M. Sancho, Noise in Spatially Extended Systems (Springer, Berlin, 1999).
6. N. J. Rao, J. D. Borwankar, and D. Ramkrishna, SIAM J. Control 12, 124 (1974).
7. R. Mannella, in Stochastic Processes in Physics, Chemistry and Biology, eds. J. A. Freun and T. Pöschel (Springer-Verlag, Berlin Heidelberg, 2000), pp. 353-364.
8. T. T. Soong, Random Differential Equations in Science and Engineering (Academic Press, 1973); S. N. Ethier and T. G. Kurtz, Markov Processes Characterization and Convergence (Wiley Series in Probability and Mathematical Statistics, 1986); L. Arnold, Stochastic Differential Equations: Theory and Applications (Wiley Interscience Publication, 1973); I.I. Gikhman and A. V. Skorokhod, Stochastic Differential Equations (Springer, 1972).
9. T. T. Soong, Random Differential Equations in Science and Engineering (Academic Press, 1973); S. N. Ethier and T. G. Kurtz, Markov Processes Characterization and Convergence (Wiley Series in Probability and Mathematical Statistics, 1986); L. Arnold, Stochastic Differential Equations: Theory and Applications (Wiley Interscience Publication, 1973); I.I. Gikhman and A. V. Skorokhod, Stochastic Differential Equations (Springer, 1972).
10. T. T. Soong, Random Differential Equations in Science and Engineering (Academic Press, 1973); S. N. Ethier and T. G. Kurtz, Markov Processes Characterization and Convergence (Wiley Series in Probability and Mathematical Statistics, 1986); L. Arnold, Stochastic Differential Equations: Theory and Applications (Wiley Interscience Publication, 1973); I.I. Gikhman and A. V. Skorokhod, Stochastic Differential Equations (Springer, 1972).
11. T. T. Soong, Random Differential Equations in Science and Engineering (Academic Press, 1973); S. N. Ethier and T. G. Kurtz, Markov Processes Characterization and Convergence (Wiley Series in Probability and Mathematical Statistics, 1986); L. Arnold, Stochastic Differential Equations: Theory and Applications (Wiley Interscience Publication, 1973); I.I. Gikhman and A. V. Skorokhod, Stochastic Differential Equations (Springer, 1972).
12. G. N. Milstein and M. V. Tret'yakov, SIAM J. Numer. Anal. 34, 2142 (1997); G. N. Milstein, Theor. Probability Appl. 30, 750 (1985).
13. G. N. Milstein and M. V. Tret'yakov, SIAM J. Numer. Anal. 34, 2142 (1997); G. N. Milstein, Theor. Probability Appl. 30, 750 (1985).
14. G. G. Batrouni, G. R. Katz, A. S. Kronfeld, G. P. Lepage, B. Svetitsky, and K. G. Wilson, Phys. Rev. D 32, 2736 (1985).
15. G. Tonnarelli, "Proprietà asintotiche di classi di algoritmi per l'integrazione di equazioni differenziali stocastiche," Dissertation for Laurea in Fisica, Pisa, 2001.
16. R. Mannella, Phys. Lett. A 254, 257 (1999).
17. W. Strittmatter, University Freiburg preprint, THEP 87/12 (1987).
18. J. M. Sancho, M. San Miguel, L. S. Katz, and J. Gunton, Phys. Rev. A 26, 1589 (1982).
19. R. Mannella and V. Palleschi, Phys. Rev. A 40, 3381 (1989).
20. R. Mannella, Fluctuations Noise Lett, 1, L45 (2001).
21. S. A. Guz, I. G. Ruzavin, and M. V. Sviridov, Slow Dynamics in Systems Driven by "Green" Noise, in Ref. 18, pp. 515-520.
22. D. Abbott and L. Kish (eds.), Unsolved Problems of Noise, AIP Conference Proceedings, Vol. 511 (Woodbury, NY, 2000).
23. S. A. Guz and M. V. Sviridov, Phys. Lett. A 240, 43 (1998).
24. L. Schimansky-Geier and Ch. Zülicke, Z. Phys. B 79, 451 (1990).
25. M. I. Dykman, R. Mannella, P. V. E. McClintock, N. D. Stein, and N. G. Stocks, Phys. Rev. E 47, 3996 (1993).
26. K. Y. R. Billah and M. Shinozuka, Phys. Rev. A 42, 7492 (1990).
27. R. Mannella and V. Palleschi, Phys. Rev. A 46, 8028 (1992); K. Y. R. Billah and M. Shinozuka, Phys. Rev. A 46, 8031 (1992).
28. R. Mannella and V. Palleschi, Phys. Rev. A 46, 8028 (1992); K. Y. R. Billah and M. Shinozuka, Phys. Rev. A 46, 8031 (1992).
29. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (CUP, Cambridge, 1986).
30. G. Marsaglia, and W. W. Tsang, SIAM J. Sci. Stat. Comp. 5, 349 (1984).
31. C. M. Luscher, Comput. Phys. Commun. 79, 100 (1994).
32. F. James, Comput. Phys. Commun. 79, 111 (1994).
33. D.E. Knuth, The Art of Computer Programming, Vol. 2 (Addison-Wesley, New York, 1981).