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On the reconstruction of the drift of a diffusion from transition probabilities which are partially observed in space

Sergio Albeverio·Carlo Marinelli
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Abstract

The problem of reconstructing the drift of a diffusion in $\erre^d$, $d\geq 2$, from the transition probability density observed outside a domain is considered. The solution of this problem also solves a new inverse problem for a class of parabolic partial differential equations. This work considerably extends \cite{jsp} in terms of generality, both concerning assumptions on the drift coefficient, and allowing for non-constant diffusion coefficient. Sufficient conditions for solvability of this type of inverse problem for $d=1$ are also given.

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Sergio Albeverio, Carlo Marinelli. 2004-10-31. On the reconstruction of the drift of a diffusion from transition probabilities which are partially observed in space. https://arxiv.org/abs/math/0411008

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