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Approximate solution of the Fokker–Planck–Kolmogorov equation
11 references·16 citing·31 second hop
Approximate solution of the Fokker–Planck–Kolmogorov equation (2002)Approximate solution of the Fokker–Planck…Stationary and non-stationary probability density function for non-linear oscillators (1997)Stationary and non-stationary…On the numerical solution of the Fokker-Planck equation for nonlinear stochastic systems (1993)On the numerical solution of …Random vibration and statistical linearization (1990)Random vibration and statisti…Random vibration and statistical linearization (1990)Random vibration and statisti…Stochastic averaging: An approximate method of solving random vibration problems (1986)Stochastic averaging: An appr…A finite element method for the statistics of non-linear random vibration (1985)A finite element method for t…Cumulant-neglect closure for non-linear oscillators under random parametric and external excitations (1984)Cumulant-neglect closure for …Approximate Method for Nonlinear Random Vibration (1975)Approximate Method for Nonlin…Probabilistic Structural Dynamics: Advanced Theory and Applications (1967)Probabilistic Structural Dyna…On the relation between ordinary and stochastic differential equations (1965)On the relation between ordin…On a Formula Concerning Stochastic Differentials (1951)On a Formula Concerning Stoch…An exponential-spectral mapping method for solving probability density evolution equations of stochastic dynamical systems (2025)An exponential-spectral mappi…Path Integral Methods for the Probabilistic Analysis of Nonlinear Systems Under a White-Noise Process (2020)Path Integral Methods for the…Wiener path integrals and multi-dimensional global bases for non-stationary stochastic response determination of structural systems (2019)Wiener path integrals and mul…Transient responses of stochastic systems under stationary excitations (2018)Transient responses of stocha…Stationary Response Probability Distribution of SDOF Nonlinear Stochastic Systems (2017)Stationary Response Probabili…A moment-equation-copula-closure method for nonlinear vibrational systems subjected to correlated noise (2016)A moment-equation-copula-clos…Numerical methods for calculating the response of a deterministic and stochastically excited Duffing oscillator (2015)Numerical methods for calcula…An Efficient Wiener Path Integral Technique Formulation for Stochastic Response Determination of Nonlinear MDOF Systems (2015)An Efficient Wiener Path Inte…Dimension Reduction of the FPK Equation via an Equivalence of Probability Flux for Additively Excited Systems (2014)Dimension Reduction of the FP…Probability density function for stochastic response of non-linear oscillation system under random excitation (2010)Probability density function …Probabilistic response of nonlinear systems under combined normal and Poisson white noise via path integral method (2010)Probabilistic response of non…Path integral solution handled by Fast Gauss Transform (2008)Path integral solution handle…Path integral solution for non-linear system enforced by Poisson White Noise (2008)Path integral solution for no…New partial differential equations governing the joint, response–excitation, probability distributions of nonlinear systems, under general stochastic excitation (2008)New partial differential equa…A homotopic approach to domain determination and solution refinement for the stationary Fokker–Planck equation (2008)A homotopic approach to domai…A Multi-Resolution Approach for Steady State Uncertainty Determination in Nonlinear Dynamical Systems (2006)A Multi-Resolution Approach f…Method for Random Vibration of Hysteretic Systems (1976)Random Vibration: A Survey of Recent Developments (1983)A general numerical solution method for Fokker-Planck equations with applications to structural reliability (1991)Numerical solutions of Fokker–Planck equation of nonlinear systems subjected to random and harmonic excitations (2011)Reliability assessment of stochastic dynamical systems using physics informed neural network based PDEM (2023)Probabilistic Theory of Structural Dynamics (1976)Introduction to Random Vibrations (1983)Efficient path integration methods for nonlinear dynamic systems (2000)Computational stochastic mechanics – recent advances (2001)First excursion probabilities for linear systems by very efficient importance sampling (2001)On stochastic differential equations (1951)Developments in stochastic structural mechanics (2006)Modeling Multibody Systems with Uncertainties. 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this work references cited by second hop

References

  • 1990Random vibration and statistical linearization995 cited
  • 1990Random vibration and statistical linearization822 cited
  • 1965On the relation between ordinary and stochastic differential equations697 cited
  • 1967Probabilistic Structural Dynamics: Advanced Theory and Applications629 cited
  • 1986Stochastic averaging: An approximate method of solving random vibration problems577 cited
  • 1951On a Formula Concerning Stochastic Differentials369 cited
  • 1993On the numerical solution of the Fokker-Planck equation for nonlinear stochastic systems289 cited
  • 1984Cumulant-neglect closure for non-linear oscillators under random parametric and external excitations234 cited
  • 1975Approximate Method for Nonlinear Random Vibration147 cited
  • 1985A finite element method for the statistics of non-linear random vibration110 cited
  • 1997Stationary and non-stationary probability density function for non-linear oscillators108 cited

Cited by

  • 2015An Efficient Wiener Path Integral Technique Formulation for Stochastic Response Determination of Nonlinear MDOF Systems86 cited
  • 2008Path integral solution for non-linear system enforced by Poisson White Noise85 cited
  • 2010Probabilistic response of nonlinear systems under combined normal and Poisson white noise via path integral method

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83 cited
  • 2014Dimension Reduction of the FPK Equation via an Equivalence of Probability Flux for Additively Excited Systems47 cited
  • 2019Wiener path integrals and multi-dimensional global bases for non-stationary stochastic response determination of structural systems47 cited
  • 2008New partial differential equations governing the joint, response–excitation, probability distributions of nonlinear systems, under general stochastic excitation31 cited
  • 2020Path Integral Methods for the Probabilistic Analysis of Nonlinear Systems Under a White-Noise Process30 cited
  • 2017Stationary Response Probability Distribution of SDOF Nonlinear Stochastic Systems29 cited
  • 2010Probability density function for stochastic response of non-linear oscillation system under random excitation27 cited
  • 2016A moment-equation-copula-closure method for nonlinear vibrational systems subjected to correlated noise20 cited
  • 2006A Multi-Resolution Approach for Steady State Uncertainty Determination in Nonlinear Dynamical Systems15 cited
  • 2008Path integral solution handled by Fast Gauss Transform14 cited
  • 2008A homotopic approach to domain determination and solution refinement for the stationary Fokker–Planck equation11 cited
  • 2025An exponential-spectral mapping method for solving probability density evolution equations of stochastic dynamical systems9 cited
  • 2018Transient responses of stochastic systems under stationary excitations9 cited
  • 2015Numerical methods for calculating the response of a deterministic and stochastically excited Duffing oscillator9 cited