. . "Onsager\u2013Machlup function"@en . . . . . . . . "1037298246"^^ . . "The Onsager\u2013Machlup 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 \u03B5 \u2192 0, where L is the Onsager\u2013Machlup function."@en . . . "The Onsager\u2013Machlup 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 \u0394ti = ti+1 \u2212 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 \u0394ti, but in the limit \u0394ti \u2192 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 \u03B5 from smooth curves \u03C61 and \u03C62 are considered: as \u03B5 \u2192 0, where L is the Onsager\u2013Machlup function."@en . . "38771161"^^ . . . . . "12140"^^ .