Communications in Mathematical Physics

, Volume 60, Issue 2, pp 153–170

The Onsager-Machlup function as Lagrangian for the most probable path of a diffusion process


  • Detlef Dürr
    • Institut für Theoretische Physik I der Universität
  • Alexander Bach
    • Institut für Theoretische Physik I der Universität

DOI: 10.1007/BF01609446

Cite this article as:
Dürr, D. & Bach, A. Commun.Math. Phys. (1978) 60: 153. doi:10.1007/BF01609446


By application of the Girsanov formula for measures induced by diffusion processes with constant diffusion coefficients it is possible to define the Onsager-Machlup function as the Lagrangian for the most probable tube around a differentiable function. The absolute continuity of a measure induced by a process with process depending diffusion w.r.t. a quasi translation invariant measure is investigated. The orthogonality of these measures w.r.t. quasi translation invariant measures is shown. It is concluded that the Onsager-Machlup function cannot be defined as a Lagrangian for processes with process depending diffusion coefficients.

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© Springer-Verlag 1978