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

DOI10.1016/J.SPA.2005.04.008arXivmath/0411008MaRDI QIDQ6474643

Sergio Albeverio, Carlo Marinelli

Publication date: 31 October 2004

Abstract: The problem of reconstructing the drift of a diffusion in $err{e}^d$, $dgeq2$, 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.

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Radon transform (44A12) Diffusion processes (60J60) Transition functions, generators and resolvents (60J35)

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