Extracting Macroscopic Stochastic Dynamics: Model Problems

Communications on Pure and Applied Mathematics

Volumn 56, Issue 2, 2003, Pages 234-269

  Huisinga, Wilhelm ^a   Schütte, Christof ^a   Stuart, Andrew M ^b  

^a FREIE UNIVERSITÄT BERLIN   (Germany)

^b UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2442444326     PISSN: 00103640     EISSN: None     Source Type: Journal    
DOI: 10.1002/cpa.10057     Document Type: Article

References (25)

1. Billingsley, P. Convergence of probability measures. Wiley, New York-London-Sydney, 1968.
2. Cano, B.; Stuart, A. M.; Süli, E.; Warren, J. O. Stiff oscillatory systems, delta jumps and white noise. Found. Comput. Math. 1 (2001), no. 1, 69-99.
3. Chorin, A. J.; Hald, O. H.; Kupferman, R. Non-Markovian optimal prediction. Phys. D, in press.
4. Dellnitz, M.; Junge, O. On the approximation of complicated dynamical behavior. SIAM J. Numer. Anal. 36 (1999), no. 2, 491-515.
5. Deuflhard, P.; Dellnitz, M.; Junge, O.; Schütte, C. Computation of essential molecular dynamics by subdivision techniques. Computational molecular dynamics: challenges, methods, ideas. Proceedings of the 2nd International Symposium on Algorithms for Macromolecular Modelling held at the Free University of Berlin, Berlin, May 21-24, 1997, 98-115. Lecture Notes in Computational Science and Engineering, 4. Springer, Berlin, 1999.
6. Deuflhard, P.; Hermans, J.; Leimkuhler, B.; Mark, A. E.; Reich, S.; Skeel, R. D., eds. Computational molecular dynamics: challenges, methods, ideas. Proceedings of the 2nd International Symposium on Algorithms for Macromolecular Modelling held at the Free University of Berlin, Berlin, May 21-24, 1997. Lecture Notes in Computational Science and Engineering, 4. Springer, Berlin, 1999.
7. Deuflhard, P.; Huisinga, W.; Fischer, A.; Schütte, C. Identification of almost invariant aggregates in reversible nearly uncoupled Markov chains. Linear Algebra Appl. 315 (2000), no. 1-3, 39-59.
8. Fischer, A.; Schütte, C.; Deuflhard, P.; Cordes. F. Hierarchical uncoupling-coupling of metastable conformations. Computational methods for macromolecules: challenges and applications-Proceedings of the 3rd International Workshop on Algorithms for Macromolecular Modelling. Lecture Notes in Computational Science and Engineering. Springer, 2002.
9. Ford, G. W.; Kac, M. On the quantum Langevin equation. J. Statist. Phys. 46 (1987), no. 5-6, 803-810.
10. Freidlin, M. I.; Wentzell, A. D. Random perturbations of dynamical systems. Grundlehren der Mathematischen Wissenschaften, 260. Springer, New York, 1984.
11. Huisinga, W. Metastability of Markovian systems: A transfer operator approach in application to molecular dynamics. Ph.D. thesis, Free University Berlin, 2001. Available at http://www.math.fu-berlin.de/~huisinga/talks/Ascona0701.pdf.
12. Kahane, J.-P. Some random series of functions. Second edition. Cambridge Studies in Advanced Mathematics, 5. Cambridge University Press, Cambridge, 1985.
13. Krylov, N.V. Introduction to the theory of diffusion processes. Translations of Mathematical Monographs, 142. American Mathematical Society, Providence, R.I., 1995.
14. Kupferman, R.; Stuart, A. M.; Terry, J. R.; Tupper, P. F. Long term behaviour of large mechanical systems with random initial data. Preprint, 2002.
15. Kurtz, T. G. A limit theorem for perturbed operator semigroups with applications to random evolutions. J. Functional Analysis 12 (1973), 55-67.
16. Majda, A. J.; Kramer, P. R. Simplified models for turbulent diffusion: theory, numerical modelling, and physical phenomena. Phys. Rep. 314 (1999), no. 4-5, 237-574.
17. Majda, A. J.; Timofeyev, I.; Vanden Eijnden, E. A mathematical framework for stochastic climate models. Comm. Pure Appl. Math. 54 (2001), no. 8, 891-974.
18. Meyn, S. P.; Tweedie, R. L. Markov chains and stochastic stability. Communications and Control Engineering Series. Springer, London, 1993.
19. Schütte, C. Conformational dynamics: modelling, theory, algorithm, and application to biomolecules. Habilitation thesis, Free University, Berlin, 1999. Available at http://www.zib.de/bib/diss/cont.de.html.
20. Schütte, C.; Fischer, A.; Huisinga, W.; Deuflhard, P. A direct approach to conformational dynamics based on hybrid Monte Carlo. Computational molecular biophysics. J. Comput. Phys. 151 (1999), no. 1, 146-168.
21. Schütte, C.; Huisinga, W. Biomolecular conformations as metastable sets of Markov chains. Proceedings of the Thirty-Eighth Annual Allerton Conference on Communication, Control, and Computing, Monticello, Illinois, 1106-1115. University of Illinois at Urbana-Champaign, 2000.
22. Schütte, C.; Huisinga, W.; Deuflhard, P. Transfer operator approach to conformational dynamics in biomolecular systems. Ergodic theory, analysis, and efficient simulation of dynamical systems, 191-223. Springer, Berlin, 2001.
23. Stuart, A. M.; Terry, J. R.; Tupper, P. F. Constructing SDEs from ODEs with random data. Stanford University Technical Report SCCM-01-04. Available at http://www-sccm.stanford.edu/wrap/pub-tech.html.
24. Stuart, A. M.; Warren, J. O. Analysis and experiments for a computational model of a heat bath. J. Statist. Phys. 97 (1999), 687-723.
25. Zwanzig, R. Nonlinear generalized Langevin equations. J. Statist. Phys. 9 (1973), 215-220.