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- Onsager–Machlup_function abstract "The Onsager–Machlup function is a function that summarizes the dynamics of a continuous stochastic process. It is used to define a probability density for a stochastic process, and it is similar to the Lagrangian of a dynamical system. It is named after Lars Onsager and S. Machlup who were the first to consider such probability densities.The dynamics of a continuous stochastic process X from time t = 0 to t = T in one dimension, satisfying a stochastic differential equationwhere W is a Wiener process,can in approximation be described by the probability density function of its value xi at a finite number of points in time ti:whereand Δti = ti+1 − ti > 0, t1 = 0 and tn = T. A similar approximation is possible for processes in higher dimensions. The approximation is more accurate for smaller time step sizes Δti, but in the limit where the time step sizes go to zero the probability density function becomes ill defined, one reason being that the product of terms diverges to infinity. In order to nevertheless define a density for the continuous stochastic process X, ratios of probabilities of X lying within a small distance ε from smooth curves φ1 and φ2 are considered:converges toas ε goes to zero, where L is the Onsager–Machlup function.".
- Onsager–Machlup_function wikiPageID "38771161".
- Onsager–Machlup_function wikiPageRevisionID "583002476".
- Onsager–Machlup_function subject Category:Functional_analysis.
- Onsager–Machlup_function subject Category:Functions_and_mappings.
- Onsager–Machlup_function subject Category:Stochastic_processes.
- Onsager–Machlup_function comment "The Onsager–Machlup function is a function that summarizes the dynamics of a continuous stochastic process. It is used to define a probability density for a stochastic process, and it is similar to the Lagrangian of a dynamical system. It is named after Lars Onsager and S.".
- Onsager–Machlup_function label "Onsager–Machlup function".
- Onsager–Machlup_function sameAs Onsager%E2%80%93Machlup_function.
- Onsager–Machlup_function sameAs Q17104894.
- Onsager–Machlup_function sameAs Q17104894.
- Onsager–Machlup_function wasDerivedFrom Onsager–Machlup_function?oldid=583002476.