The Onsager-Machlup Lagrangian and the Optimal Control for Diffusion Processes

  • Kunio Yasue


A basic role of the Onsager-Machlup Lagrangian as the cost functional for the stochastic control problem is clarified. It is found that any n-dimensional nonlinear diffusion process described by a class of stochastic differential equation of Itô type can be regarded as if it were controlled optimally by the Onsager-Machlup Lagrangian. It is shown that the deterministic path of the diffusion process in the small fluctuation (infinite volume) limit coincides with the most probable path. An outlook on the stochastic control theoretical formulation of the vacuum tunneling phenomena in non-Abelian gauge theory is also presented hoping that it will help us to understand the quantum vacuum structure in quantum chromodynamies profoundly.


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Copyright information

© Plenum Press, New York 1980

Authors and Affiliations

  • Kunio Yasue
    • 1
  1. 1.Département de Physique ThéoriqueUniversité de GenèveGenève 4Switzerland

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