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Reconstructing the drift of a diffusion from partially observed transition probabilities

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  • Albeverio, S.
  • Marinelli, C.

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.

Suggested Citation

  • Albeverio, S. & Marinelli, C., 2005. "Reconstructing the drift of a diffusion from partially observed transition probabilities," Stochastic Processes and their Applications, Elsevier, vol. 115(9), pages 1487-1502, September.
    • Handle: RePEc:eee:spapps:v:115:y:2005:i:9:p:1487-1502
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    References listed on IDEAS

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    1. Qian, Zhongmin & Zheng, Weian, 2004. "A representation formula for transition probability densities of diffusions and applications," Stochastic Processes and their Applications, Elsevier, vol. 111(1), pages 57-76, May.
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