The role of the Onsager–Machlup Lagrangian in the theory of stationary diffusion process
- 1 September 1979
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 20 (9) , 1861-1864
- https://doi.org/10.1063/1.524303
Abstract
The Onsager–Machlup Lagrangian is shown to have a direct relevance to a cost function for a stochastic control problem. It is found that any stationary diffusion process can be regarded as a solution to the stochastic control problem, that is, it is controlled optimally by the Onsager–Machlup Lagrangian. A deterministic limit of the stationary diffusion process is also obtained as a solution to an ordinary (nonrandom) control problem which is equivalent to the usual variational problem with respect to the Onsager–Machlup Lagrangian.Keywords
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