Analysis of SPDEs arising in path sampling. Part I: The Gaussian case
作者： M. Hairer , A. M. Stuart , J. Voss , P. Wiberg
DOI: 10.4310/CMS.2005.V3.N4.A8
关键词:
摘要: In many applications it is important to be able sample paths of SDEs conditional on observations various kinds. This paper studies SPDEs which solve such sampling problems. The SPDE may viewed as an infinite dimensional analogue the Langevin SDE used in finite sampling. Here theory developed for conditioned Gaussian processes resulting linear. Applications include Kalman-Bucy filter/smoother. A companion nonlinear case, building linear analysis provided here.
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G. Da Prato, J. Zabczyk, Ergodicity for infinite dimensional systems Cambridge University Press. ,(1996) , 10.1017/CBO9780511662829
Giuseppe Da Prato, Jerzy Zabczyk, Stochastic Equations in Infinite Dimensions ,(1992)
Steven E. Shreve, Ioannis Karatzas, Brownian Motion and Stochastic Calculus ,(1987)
Shing Tung Yau, Mathematics and its applications international conference on control and automation. pp. 9- 10 ,(2002) , 10.1109/ICCA.2002.1229256
Volker Betz, József Lőrinczi, Uniqueness of Gibbs measures relative to Brownian motion Annales De L Institut Henri Poincare-probabilites Et Statistiques. ,vol. 39, pp. 877- 889 ,(2003) , 10.1016/S0246-0203(03)00021-9
George Casella, Christian P. Robert, Monte Carlo Statistical Methods ,(1999)
I. Iscoe, M. B. Marcus, D. McDonald, M. Talagrand, J. Zinn, Continuity of $l^2$-Valued Ornstein-Uhlenbeck Processes Annals of Probability. ,vol. 18, pp. 68- 84 ,(1990) , 10.1214/AOP/1176990938
Andrew M. Stuart, Jochen Voss, Petter Wilberg, Conditional Path Sampling of SDEs and the Langevin MCMC Method Communications in Mathematical Sciences. ,vol. 2, pp. 685- 697 ,(2004) , 10.4310/CMS.2004.V2.N4.A7
Maria G. Reznikoff, Eric Vanden-Eijnden, None, Invariant measures of stochastic partial differential equations and conditioned diffusions Comptes Rendus Mathematique. ,vol. 340, pp. 305- 308 ,(2005) , 10.1016/J.CRMA.2004.12.025
Robert J. Adler, The Geometry of Random Fields ,(2010)