This paper uses Lie symmetry methods to calculate certain expectations for a large class of Itô diffusions. We show that if the problem has sufficient symmetry, then the problem of computing functionals of the form Ex(e−λXt−∫0tg(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.
Publié le : 2009-02-15
Classification:
Lie symmetry groups,
fundamental solutions,
diffusion processes,
transition densities,
expectations and functionals,
35C05,
35K15,
60H99,
60G99
@article{1235140335,
author = {Craddock, Mark and Lennox, Kelly A.},
title = {The calculation of expectations for classes of diffusion processes by Lie symmetry methods},
journal = {Ann. Appl. Probab.},
volume = {19},
number = {1},
year = {2009},
pages = { 127-157},
language = {en},
url = {http://dml.mathdoc.fr/item/1235140335}
}
Craddock, Mark; Lennox, Kelly A. The calculation of expectations for classes of diffusion processes by Lie symmetry methods. Ann. Appl. Probab., Tome 19 (2009) no. 1, pp. 127-157. http://gdmltest.u-ga.fr/item/1235140335/