Projecting the Fokker-Planck Equation onto a finite dimensional exponential family

Damiano Brigo; Giovanni Pistone

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arXiv · 0901.1308

Projecting the Fokker-Planck Equation onto a finite dimensional exponential family

Damiano Brigo·Giovanni Pistone

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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.

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Damiano Brigo, Giovanni Pistone. 2009-01-09. Projecting the Fokker-Planck Equation onto a finite dimensional exponential family. https://arxiv.org/abs/0901.1308

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