Reconstructing the drift of a diffusion from partially observed transition probabilities

S. Albeverio and C. Marinelli

Stochastic Processes and their Applications, 2005, vol. 115, issue 9, 1487-1502

Abstract: The problem of reconstructing the drift of a diffusion in , d[greater-or-equal, slanted]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 [S. Albeverio et al. J. Statist. Phys. 57(1-2) (1989) 347-356] 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.

Keywords: Inverse; problems; Stochastic; differential; equations; X-ray; transform; Schrodinger; operators; Elliptic; operators (search for similar items in EconPapers)
Date: 2005
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