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
Posted ContentDOI
Beyond Brownian motion and the Ornstein-Uhlenbeck process: Stochastic diffusion models for the evolution of quantitative characters
TL;DR: New, non-Gaussian stochastic differential equation (diffusion) models of quantitative trait evolution and diversification are described and general methods for deriving new diffusion models are presented.
Journal ArticleDOI
Learning Curves for Deep Neural Networks: A Gaussian Field Theory Perspective.
Omry Cohen,Or Malka,Zohar Ringel +2 more
TL;DR: This work constructs a versatile field-theory formalism for supervised deep learning, involving renormalization group, Feynmann diagrams, and replicas, and shows that this approach leads to highly accurate predictions of learning curves of truly deep DNNs trained on polynomial regression problems.
Journal ArticleDOI
Gibrat’s Law Redux: think profitability instead of growth
TL;DR: The authors show that the diffusion of profit rates applies across all surviving corporations, irrespective of their size or industry, which is not true for growth rates, since the idiosyncratic efforts merely affect the individual persistence of abnormal profits from the systemwide norm.
Journal ArticleDOI
Reactive Random Walk Particle Tracking and Its Equivalence With the Advection-Diffusion-Reaction Equation
TL;DR: In this paper, the authors acknowledge the support of the European Research Council (ERC) through the project MHetScale (617511) and the Spanish Ministry of Economy, Industry and Competitiveness, and European Regional Development Fund through project MECMAT (CGL2016•80022•R).
Journal ArticleDOI
Natural Transform for Solving Fractional Models
TL;DR: In this article, a domain decomposition natural transform method (ADNTM) is proposed to obtain approximate analytical solution of fractional physical models, which is based on a combination of a Domain Decomposition method and a Natural Transform method.
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.