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- 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 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 equation where 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: where and 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 Δti → 0 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: as ε → 0, where L is the Onsager–Machlup function. (en)
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- 12429 (xsd:nonNegativeInteger)
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- 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 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 equation where as ε → 0, where L is the Onsager–Machlup function. (en)
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- Onsager–Machlup function (en)
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