| Author(s) |
Damiano Brigo ( )1, Giovanni Pistone () |
| Laboratory |
|
| Subject |
Mathematics/Probability
|
| Title |
Projecting the Fokker-Planck Equation onto a finite dimensional exponential family |
| Abstract |
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. |
| Fulltext language |
English |
| Production date |
1996-07-01 |
|
| Keyword(s) |
Nonlinear diffusions – Fokker-Planck equation – finite dimensional families – exponential families – stochastic differential equations – Fisher metric – differential geometry and statistics – convergence. |
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