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

2004/10/31 by Sergio Albeverio, Albeverio, Sergio, Carlo Marinelli +1
Computer Science · Economics, Econometrics and Finance · Mathematics · #35R30 #44A12 #60J60 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Numerical methods in inverse problems #Primary 62M99 #Probability (math.PR) #Secondary 60J35 #Statistics Theory (math.ST) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.math/0411008

openalex publication_date 2004/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The problem of reconstructing the drift of a diffusion in \erre^d, d≥ 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 \citejsp 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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