Sampling conditioned hypoelliptic diffusions

Annals of Applied Probability

Volumn 21, Issue 2, 2011, Pages 669-698

  Hairer, Martin ^a   Stuart, Andrew M ^a   Voss, Jochen ^b  

^a UNIVERSITY OF WARWICK   (United Kingdom)

^b UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

Conditioned stochastic ordinary differential equations; Fourth order SPDEs; Hypoelliptic diffusions; Stochastic partial differential equations

Indexed keywords

EID: 79953289665     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/10-AAP708     Document Type: Article

References (19)

1. APTE, A., HAIRER, M., STUART, A. M. and VOSS, J. (2007). Sampling the posterior: An approach to non-Gaussian data assimilation. Phys. D 230 50-64. MR2345202 (Pubitemid 46776902)
2. BLÖMKER, D.,MAIER-PAAPE, S. andWANNER, T. (2001). Spinodal decomposition for the Cahn-Hilliard-Cook equation. Comm. Math. Phys. 223 553-582. MR1866167
3. DA PRATO, G. and DEBUSSCHE, A. (1996). Stochastic Cahn-Hilliard equation. Nonlinear Anal. 26 241-263. MR1359472 (Pubitemid 126401727)
4. DA PRATO, G. and ZABCZYK, J. (1992). Stochastic Equations in Infinite Dimensions. Encyclopedia of Mathematics and Its Applications 44. Cambridge Univ. Press, Cambridge. MR1207136
5. HAIRER, M. (2009). An introduction to stochastic PDEs. Available at http://arxiv.org/abs/0907. 4178.
6. HAIRER, M. (2010). Singular perturbations to semilinear stochastic heat equations. Preprint. Available at http://arxiv.org/abs/1002.3722.
7. HAIRER, M., STUART, A. M. and VOSS, J. (2007). Analysis of SPDEs arising in path sampling. II. The nonlinear case. Ann. Appl. Probab. 17 1657-1706. MR2358638
8. HAIRER, M., STUART, A. M., VOSS, J. andWIBERG, P. (2005). Analysis of SPDEs arising in path sampling. I. The Gaussian case. Commun. Math. Sci. 3 587-603. MR2188686
9. HAIRER, M., STUART, A. and VOSS, J. (2009). Sampling conditioned diffusions. In Trends in Stochastic Analysis. London Mathematical Society Lecture Note Series 353 159-185. Cambridge Univ. Press, Cambridge. MR2562154
10. KATO, T. (1966). Perturbation Theory for Linear Operators. Springer, Berlin.
11. LAURITSEN, K. B., CUERNO, R. and MAKSE, H. A. (1996). Noisy Kuramoto-Sivashinsky equation for an erosion model. Phys. Rev. E 54 3577-3580. (Pubitemid 126584241)
12. RÖCKNER, M. andMA, Z. M. (1992). Introduction to the Theory of (nonsymmetric) Dirichlet Forms. Springer, Berlin. MR1214375
13. REED, M. and SIMON, B. (1972). Methods of Modern Mathematical Physics. I. Functional Analysis. Academic Press, New York. MR0493419
14. REZNIKOFF, M. G. andVANDEN-EIJNDEN, E. (2005). Invariant measures of stochastic partial differential equations and conditioned diffusions. C. R. Math. Acad. Sci. Paris 340 305-308. MR2121896 (Pubitemid 40262426)
15. STUART, A. M., VOSS, J. and WIBERG, P. (2004). Conditional path sampling of SDEs and the Langevin MCMC method. Commun. Math. Sci. 2 685-697. MR2119934
16. TRIEBEL, H. (1983). Theory of Function Spaces. Monographs in Mathematics 78. Birkhäuser, Basel. MR0781540
17. TRIEBEL, H. (1992). Theory of Function Spaces. II. Monographs in Mathematics 84. Birkhäuser, Basel. MR1163193
18. TRIEBEL, H. (2006). Theory of Function Spaces. III. Monographs in Mathematics 100. Birkhäuser, Basel. MR2250142
19. ZABCZYK, J. (1989). Symmetric solutions of semilinear stochastic equations. In Stochastic Partial Differential Equations and Applications, II (Trento, 1988). Lecture Notes in Math. 1390 237-256. Springer, Berlin. MR1019609