The calculation of expectations for classes of diffusion processes by Lie symmetry methods
| dc.creator | Craddock, Mark | |
| dc.creator | Lennox, Kelly A. | |
| dc.date | 2009-02-27 | |
| dc.date.accessioned | 2026-07-07T12:47:35Z | |
| dc.date.available | 2026-07-07T12:47:35Z | |
| dc.description | 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 $E_x(e^{-λX_t-\int_0^tg(X_s) ds})$ 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. | |
| dc.description | Published in at http://dx.doi.org/10.1214/08-AAP534 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/0902.4806 | |
| dc.identifier | http://arxiv.org/abs/0902.4806 | |
| dc.identifier | Annals of Applied Probability 2009, Vol. 19, No. 1, 127-157 | |
| dc.identifier | doi:10.1214/08-AAP534 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/221768 | |
| dc.subject | Probability | |
| dc.subject | 35C05, 35K15, 60H99, 60G99 (Primary) | |
| dc.title | The calculation of expectations for classes of diffusion processes by Lie symmetry methods | |
| dc.type | text |