Methodology for the solutions of some reduced Fokker-Planck equations in high dimensions

DOI10.1002/andp.201010465zbMath1214.82076OpenAlexW2074012856MaRDI QIDQ3084640

Guo-Kang Er

Publication date: 25 March 2011

Published in: Annalen der Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/andp.201010465

zbMATH Keywords

Fokker-Planck equationlarge-scale systemsnonlinear stochastic dynamicsstate space split

Mathematics Subject Classification ID

Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Fokker-Planck equations (35Q84)

Related Items (11)

Probabilistic solutions of some multi-degree-of-freedom nonlinear stochastic dynamical systems excited by filtered Gaussian white noise ⋮ Probabilistic response of nonsmooth nonlinear systems under Gaussian white noise excitations ⋮ A highly-efficient method for stationary response of multi-degree-of-freedom nonlinear stochastic systems ⋮ Transient probability density of nonlinear oscillator under parametric harmonic and external modulated stochastic excitations ⋮ Efficient statistically accurate algorithms for the Fokker-Planck equation in large dimensions ⋮ Probabilistic solution for an MDOF hysteretic degrading system to modulated non-stationary excitations ⋮ A generalized method for the stationary probabilistic response of nonlinear dynamical system ⋮ Rigorous Analysis for Efficient Statistically Accurate Algorithms for Solving Fokker--Planck Equations in Large Dimensions ⋮ Probabilistic solutions of nonlinear oscillators excited by combined colored and white noise excitations ⋮ Probabilistic solutions of nonlinear oscillators to subject random colored noise excitations ⋮ Stochastic response of MDOF system to non-stationary random excitation

Cites Work

• Maximum entropy principle and nonlinear stochastic oscillators
• Probability amplitude structure of Fokker-Planck equation
• Über die analytischen Methoden in der Wahrscheinlichkeitsrechnung
• An exact solution to a certain nonlinear random vibration problem
• The Probabilistic Solutions to Nonlinear Random Vibrations of Multi-Degree-of-Freedom Systems
• Simulation of multivariable non-linear stochastic systems
• Approximate analysis of non-linear stochastic systems
• Singular Perturbation Analysis of the Fokker–Planck Equation: Kramers’ Underdamped Problem
• Asymptotic Series for Singularly Perturbed Kolmogorov–Fokker–Planck Equations
• Brownian motion in a field of force and the diffusion model of chemical reactions

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