Large deviations for multiscale diffusion via weak convergence methods

Stochastic Processes and their Applications

Volumn 122, Issue 4, 2012, Pages 1947-1987

  Dupuis, Paul ^a   Spiliopoulos, Konstantinos ^a  

^a BROWN UNIVERSITY   (United States)

Author keywords

Importance sampling; Large deviations; Multiscale diffusion; Rugged energy landscape

Indexed keywords

ACTION FUNCTIONAL; ENERGY LANDSCAPE; HOMOGENIZATION PARAMETERS; LARGE DEVIATIONS; LOWER BOUNDS; MULTISCALE DIFFUSION; MULTISCALES; NOISE DIFFUSION; WEAK CONVERGENCE;

COMPUTER SIMULATION; STATISTICS; STOCHASTIC SYSTEMS;

IMPORTANCE SAMPLING;

EID: 84858713706     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2011.12.006     Document Type: Article

References (46)

1. M. Arisawa, and P.-L. Lions On ergodic stochastic control Communications in Partial Differential Equations 23 11 1998 333 358
2. Z. Artstein, and A. Vigodner Singularly perturbed ordinary differential equations with dynamic limits Proceedings of the Royal Society of Edinburgh 126 1996 541 569 Section A
3. A. Ansari Mean first passage time solution of the Smoluchowski equation: application of relaxation dynamics in myoglobin Journal of Chemical Physics 112 5 2000 2516 2522
4. A. Arapostathis, V.S. Borkar, M.K. Ghosh, Ergodic Control of Diffusion Processes, Cambridge University press (in press).
5. P. Baldi Large deviations for diffusions processes with homogenization and applications Annals of Probability 19 2 1991 509 524
6. A. Bensoussan, J.L. Lions, and G. Papanicolaou Studies in Mathematics and its Applications Asymptotic Analysis for Periodic Structures vol. 5 1978 North-Holland Publishing Co. Amsterdam
7. Rn Journal fr die Reine und Angewandte Mathematik 429 1992 125 160
8. V. Borkar, and V. Gaitsgory Averaging of singularly perturbed controlled stochastic differential equations Applied Mathematics and Optimization 56 2 2007 169 209
9. M. Boué, and P. Dupuis A variational representation for certain functionals of Brownian motion Annals of Probability 26 4 1998 1641 1659
10. M. Boué, P. Dupuis, and R.S. Ellis Large deviations for small noise diffusions with discontinuous statistics Probability Theory and Related Fields 116 1 2000 125 149
11. J.D. Bryngelson, J.N. Onuchic, N.D. Socci, and P.G. Wolynes Funnels, pathways and the energy landscape of protein folding: a synthesis Proteins 21 3 1995 167 195
12. R. Buckdahn, Y. Hu, and S. Peng Probabilistic approach to homogenization of viscosity solutions of parabolic PDE's Nonlinear Differential Equations and Applications 6 4 1999 395 411
13. A. Budhiraja, and P. Dupuis A variational representation for positive functionals of infinite dimensional Brownian motion Probability and Mathematical Statistics 20 2000 39 61 Fasc. 1
14. P. Dupuis, and R.S. Ellis A Weak Conergence Approach to the Theory of Large Deviations 1997 John Wiley & Sons New York
15. P. Dupuis, K. Spiliopoulos, H. Wang, Importance sampling for multiscale diffusions, Preprint, 2011.
16. S.N. Eithier, and T.G. Kurtz Markov Processes: Characterization and Convergence 1986 John Wiley & Sons New York
17. M. Freidlin, and R. Sowers A comparison of homogenization and large deviations, with applications to wavefront propagation Stochastic Process and Their Applications 82 1 1999 23 52
18. V. Gaitsgory On a representation of the limit occupational measures set of a control system with applications to singularly perturbed control systems SIAM Journal on Control and Optimization 43 1 2004 325 340
19. V. Gaitsgory, and M.-T. Nguyen Multiscale singularly perturbed control systems: limit occupational measures sets and averaging SIAM Journal on Control and Optimization 41 3 2002 954 974
20. D. Gilbarg, and N.S. Trudinger Elliptic Partial Differential Equations of Second Order second ed. 1983 Springer-Verlag
21. C. Hyeon, and D. Thirumalai Can energy landscapes roughness of proteins and RNA be measured by using mechanical unfloding experiments? Proceedings of the National Academy of Sciences of the United States of America 100 18 2003 10249 10253
22. I. Karatzas, and S.E. Shreve Brownian Motion and Stochastic Calculus second ed. 2000 Springer-Verlag
23. H. Kaise, and S.J. Sheu On the structure of solutions of ergodic type Bellman equation related to risk-sensitive control Annals of Probability 34 1 2006 284 320
24. T.G. Kurtz, and R.H. Stockbridge Existence of Markov controls and characterization of optimal Markov controls SIAM Journal on Control and Optimization 36 2 1998 609 653
25. H.J. Kushner Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems 1990 Birkhuser Boston, Basel, Berlin
26. H.J. Kushner Large deviations for two-time-scale diffusions with delays Applied Mathematics and Optimization 62 3 2010 295 322
27. R. Lipster Large deviations for two scaled diffusions Probability Theory and Related Fields 106 1 1996 71 104
28. S. Lifson, and J.L. Jackson On the self-diffusion of ions in a polyelectrolyte solution Journal of Chemical Physics 36 1962 2410 2414
29. D. Mondal, P.K. Ghosh, and D.S. Ray Noise-induced transport in a rough ratcket potential Journal of Chemical Physics 130 2009 074703.1 074703.7
30. E. Pardoux, and A.Yu. Veretennikov On Poisson equation and diffusion approximation 2 Annals of Probability 31 3 2003 1166 1192
31. R.T. Rockafellar Convex Analysis 1970 Princeton Landmarks in Mathematics and Physics
32. J.G. Saven, J. Wang, and P.G. Wolynes Kinetics of protein folding: the dynamics of globally connected rough energy landscapes with biases Journal of Chemical Physics 101 12 1994 11037 11043
33. A.Yu. Veretennikov, On large deviations in the averaging principle for SDEs with a full dependence, correction, arXiv:math/0502098v1 [math.PR] (2005). initial article in Annals of Probability, Vol. 27, No. 1, (1999), pp. 284-296.
34. A.Yu. Veretennikov On large deviations for SDEs with small diffusion and averaging Stochastic Processes and Their Applications 89 1 2000 69 79
35. R. Zwanzig Diffusion in a rough potential Proceedings of the National Academy of Sciences of the United States of America 85 1988 2029 2030
36. O. Alvarez, and M. Bardi Viscosity solutions methods for singular perturbations in deterministic and stochastic control SIAM Journal on Control and Optimization 40 4 2001 1159 1188
37. Z. Artstein, and V. Gaitsgory Tracking fast trajectories along a slow dynamics: a signular perturbation analysis SIAM Journal on Control and Optimization 35 5 1997 1487 1507
38. Z. Artstein, and V. Gaitsgory The value function of singularly perturbed control systems Applied Mathematics and Optimization 41 3 2000 425 445
39. V. Borkar Optimal Control of Diffusion Processes Pitman Research Notes in Mathematics Series vol. 203 1989 Longman scientific and technical Harlow, UK
40. V. Borkar, and V. Gaitsgory On existence of limit occupational measures set of a controlled stochastic differential equation SIAM Journal on Control and Optimization 44 4 2005 1436 1473
41. K. Horie, and H. Ishii Simultaneous effects of homogenization and vanishing viscosity in fully nonlinear elliptic equations Funkcialaj Ekvacioj 46 1 2003 63 88
42. R.Z. Khasminiskii Ergodic properties of recurrent diffusion processes and stabilization of the solution to the Cauchy problem for parabolic equations Theory of Probability and its Applications 5 2 1960 179 196
43. R.Z. Khasminiskii Stochastic Stability of Differential Equations second ed. 1980 Kluwer Academic Publishers
44. H.J. Kushner, and P. Dupuis Numerical Methods for Stochastic Control Problems in Continuous Time second ed. 2000 Springer
45. J.R. Norris Long time behaviour of heat flow: global estimates and exact asymptotics Archive for Rational Mechanics and Analysis 140 1997 161 195
46. M. Robin Long-time average cost control problems for continuous time Markov processes: a survey Acta Applicandae Mathemtiticae 1 1983 281 299