Projecting the Fokker-Planck Equation onto a finite dimensional exponential family
| dc.creator | Brigo, Damiano | |
| dc.creator | Pistone, Giovanni | |
| dc.date | 2009-01-09 | |
| dc.date.accessioned | 2026-07-07T12:28:07Z | |
| dc.date.available | 2026-07-07T12:28:07Z | |
| dc.description | In the present paper we discuss problems concerning evolutions of densities related to Ito diffusions in the framework of the statistical exponential manifold. We develop a rigorous approach to the problem, and we particularize it to the orthogonal projection of the evolution of the density of a diffusion process onto a finite dimensional exponential manifold. It has been shown by D. Brigo (1996) that the projected evolution can always be interpreted as the evolution of the density of a different diffusion process. We give also a compactness result when the dimension of the exponential family increases, as a first step towards a convergence result to be investigated in the future. The infinite dimensional exponential manifold structure introduced by G. Pistone and C. Sempi is used and some examples are given. | |
| dc.identifier | https://arxiv.org/abs/0901.1308 | |
| dc.identifier | http://arxiv.org/abs/0901.1308 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/215433 | |
| dc.subject | Probability | |
| dc.title | Projecting the Fokker-Planck Equation onto a finite dimensional exponential family | |
| dc.type | text |