Cubature on Wiener space

被引：127
作者：
Lyons, T [1 ]
Victoir, N [1 ]
机构：
[1] Univ Oxford, Inst Math, Oxford OX1 3LB, England
来源：
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2004年 / 460卷 / 2041期
基金：
英国工程与自然科学研究理事会;
关键词：
cubature formulae; stochastic analysis; Chen series;
D O I：
10.1098/rspa.2003.1239
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
It is well known that there is a mathematical equivalence between 'solving' parabolic partial differential equations (PDEs) and 'the integration' of certain functionals on Wiener space. Monte Carlo simulation of stochastic differential equations (SDEs) is a naive approach based on this underlying principle. In finite dimensions, it is well known that cubature can be a very effective approach to integration. We discuss the appropriate extension of this idea to Wiener space. In the process we develop high-order numerical schemes valid for high-dimensional SDEs and semi-elliptic PDEs.
引用
收藏
页码：169 / 198
页数：30
相关论文
共 18 条
[1]  
BENAROUS G, 1989, PROBAB THEORY REL, V81, P29
[2]   INTEGRATION OF PATHS, GEOMETRIC INVARIANTS AND A GENERALIZED BAKER-HAUSDORFF FORMULA [J].
CHEN, KT .
ANNALS OF MATHEMATICS, 1957, 65 (01) :163-178
[3]  
Fawcett T., 2003, THESIS U OXFORD UK
[4]  
Gelfand I., 1963, CALCULUS VARIATIONS
[5]  
Gromov M., 1996, Sub-Riemannian geometry, V144, P79, DOI DOI 10.1007/978-3-0348-9210-0_2
[6]  
IKEDA N, 1981, STOCHASTIC DIFFERENT, P24
[7]  
Kloeden P. E., 1992, Appl. Math. (N. Y.), V23
[8]  
KUNITA H, 1980, LECT NOTES MATH, V784, P282
[9]  
KUSUOKA S, 1998, ADV STUDIES PURE MAT, V31, P147
[10]  
KUSUOKA S., 1987, J FAC SCI U TOKYO 1A, VA34, P391
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