Green's Functions by Monte Carlo

被引：0

作者：

White, David ^{[1
]}

Stuart, Andrew ^{[1
]}

机构：

[1] Univ Warwick, Math Inst, Coventry CV4 7AL, Warwick, England

来源：

MONTE CARLO AND QUASI-MONTE CARLO METHODS 2008 | 2009年

关键词：

SPDES;

D O I：

10.1007/978-3-642-04107-5_41

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We describe a new numerical technique to estimate Green's functions of elliptic differential operators on bounded open sets. The algorithm utilizes SPDE based function space sampling techniques in conjunction with Metropolis-Hastings MCMC. The key idea is that neither the proposal nor the acceptance probability require the evaluation of a Dirac measure. The method allows Green's functions to be estimated via ergodic averaging. Numerical examples in both 1D and 2D, with second and fourth order elliptic PDE's, are presented to validate this methodology.

引用

页码：627 / 636

页数：10

共 9 条

[1] Barton G, 1989, Elements of Green's functions and propagation: potentials, diffusion, and waves
[2] BECK JV, 1992, THERMAL SCI
[3] MCMC methods for diffusion bridges
Beskos, Alexandros
Roberts, Gareth
Stuart, Andrew
Voss, Jochen
[J]. STOCHASTICS AND DYNAMICS, 2008, 8 (03) : 319 - 350
[4] Analysis of spdes arising in path sampling part II: The nonlinear case
Hairer, M.
Stuart, A. M.
Voss, J.
[J]. ANNALS OF APPLIED PROBABILITY, 2007, 17 (5-6) : 1657 - 1706
[5] Hairer M, 2005, COMMUN MATH SCI, V3, P587
[6] HASTINGS WK, 1970, BIOMETRIKA, V57, P97, DOI 10.1093/biomet/57.1.97
[7] ROACH GF, 1982, GREENS FUNCTIONS SEC
[8] WHITE D, 2009, THESIS INFINITE DIME
[9] Zabczyk, 1992, STOCHASTIC EQUATIONS, V44

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