THE CALCULATION OF EXPECTATIONS FOR CLASSES OF DIFFUSION PROCESSES BY LIE SYMMETRY METHODS
成果类型：
Article
署名作者：
Craddock, Mark; Lennox, Kelly A.
署名单位：
University of Technology Sydney
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/08-AAP534
发表日期：
2009
页码：
127-157
关键词：
摘要：
This paper uses Lie symmetry methods to calculate certain expectations for a large class of Ito diffusions. We show that if the problem has sufficient symmetry, then the problem of computing functionals of the form E-x(e(-lambda Xt-f0tg(Xs)ds)) can be reduced to evaluating a single integral of known functions. Given a drift f we determine the functions g for which the corresponding functional can be calculated by symmetry. Conversely, given g, we can determine precisely those drifts f for which the transition density and the functional may be computed by symmetry. Many examples are presented to illustrate the method.