Book ChapterDOI
Fokker-Planck Equation
Hannes Risken
- pp 63-95
Reads0
Chats0
TLDR
In this paper, an equation for the distribution function describing Brownian motion was first derived by Fokker [11] and Planck [12] and it is shown that expectation values for nonlinear Langevin equations (367, 110) are much more difficult to obtain.Abstract:
As shown in Sects 31, 2 we can immediately obtain expectation values for processes described by the linear Langevin equations (31, 31) For nonlinear Langevin equations (367, 110) expectation values are much more difficult to obtain, so here we first try to derive an equation for the distribution function As mentioned already in the introduction, a differential equation for the distribution function describing Brownian motion was first derived by Fokker [11] and Planck [12]: many review articles and books on the Fokker-Planck equation now exist [15 – 15]read more
Citations
More filters
Journal ArticleDOI
An efficient method for simulation of noisy coupled multi-dimensional oscillators
TL;DR: This work presents an efficient computational method by taking a population density approach in which the probability density of observing an oscillator at a point of state space is the primary variable instead of the states of all of the oscillators.
Journal ArticleDOI
Fluctuation theorem for irreversible entropy production in electrical conduction
TL;DR: In this article , it was shown that the negative rates are fully compatible with stochastic thermodynamics, namely, that the entropy production does fulfill a fluctuation theorem, and the analysis was concluded with the observation that the statistical entropy production as defined by the surprisal or ignorance of the Shannon information does not agree with the phenomenological approach.
Journal ArticleDOI
Bayesian inference for a susceptible-exposed-infected-recovered epidemic model with data augmentation
TL;DR: A Bayesian data-augmentation method allows estimating the parameters in a susceptible-exposed-infected-recovered (SEIR) epidemic model, which is formulated as a continuous-time Markov process and approximated by a diffusion process using the convergence of the master equation.
Journal ArticleDOI
Probabilistic Algorithm for Ballistic Parachute Transition Altitude Optimization
Andrew Leonard,Benjamin Klein,Chris Jumonville,Jonathan Rogers,Adam R. Gerlach,David B. Doman +5 more
TL;DR: A probabilistic algorithm for the optimization of drogue-to-main parachute transition altitude is proposed for high-altitude, low-opening ballistic airdrop.
Journal ArticleDOI
Numerical path integral calculation of the probability function and exit time: an application to non-gradient drift forces
TL;DR: Numerical solutions based on the path integral representation of stochastic processes for non-gradient drift Langevin forces in the presence of noise are provided to follow the temporal evolution of the probability density function and to compute exit times even for arbitrary noise.
References
More filters
Journal ArticleDOI
Fluctuations and Irreversible Processes
Lars Onsager,S. Machlup +1 more
TL;DR: In this paper, the probability of a given succession of (nonequilibrium) states of a spontaneously fluctuating thermodynamic system is calculated, on the assumption that the macroscopic variables defining a state are Gaussian random variables whose average behavior is given by the laws governing irreversible processes.
Journal ArticleDOI
The Radiation Theories of Tomonaga, Schwinger, and Feynman
TL;DR: In this article, a unified development of the subject of quantum electrodynamics is outlined, embodying the main features both of the Tomonaga-Schwinger and of the Feynman radiation theory.
Journal ArticleDOI
Covariant formulation of non-equilibrium statistical thermodynamics
TL;DR: In this paper, the diffusion matrix of the Fokker Planck equation is used as a contravariant metric tensor in phase space, and the covariance of the Langevin-equations and the fokker equation is demonstrated.
Journal ArticleDOI
Approximation of the Linear Boltzmann Equation by the Fokker-Planck Equation
TL;DR: In this article, the first two terms of the Kramers-Moyal expansion of the Fokker-Planck equation were used to approximate the linear Boltzmann integral operator.