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Dimension-reduction of FPK equation via equivalent drift coefficient
8 references·5 citing·32 second hop
Dimension-reduction of FPK equation via equivalent drift coefficient (2014)Dimension-reduction of FPK equation via e…Reliability assessment in structural dynamics (2013)Reliability assessment in str…Random Vibrations: Analysis of Structural and Mechanical Systems (2011)Random Vibrations: Analysis o…Advances of the probability density evolution method for nonlinear stochastic systems (2011)Advances of the probability d…Stochastic Dynamics of Structures (2009)Stochastic Dynamics of Struct…A note on the principle of preservation of probability and probability density evolution equation (2008)A note on the principle of pr…The principle of preservation of probability and the generalized density evolution equation (2006)The principle of preservation…Efficient path integration methods for nonlinear dynamic systems (2000)Efficient path integration me…Simulation of Stochastic Processes by Spectral Representation (1991)Simulation of Stochastic Proc…Stochastic dynamic response analysis via dimension-reduced probability density evolution equation (DR-PDEE) with enhanced tail-accuracy (2025)Stochastic dynamic response a…Efficient stochastic response analysis of high-dimensional nonlinear systems subject to multiplicative noise via the DR-PDEE (2025)Efficient stochastic response…DR-PDEE-based probabilistic response analysis for high-dimensional nonlinear dynamical systems under general non-white and non-stationary random excitations via constructing the auxiliary diffusion process (2025)DR-PDEE-based probabilistic r…Dimension-reduced Chapman-Kolmogorov equation for high-dimensional stochastic dynamical systems (2025)Dimension-reduced Chapman-Kol…Physically Driven Exact Dimension Reduction of a Class of Nonlinear Multidimensional Systems Subjected to Additive White Noise (2022)Physically Driven Exact Dimen…Digital simulation of random processes and its applications (1972)Method for Random Vibration of Hysteretic Systems (1976)Stochastic Finite Elements: A Spectral Approach (1991)Probability density evolution method: Background, significance and recent developments (2015)Dynamic reliability analysis using the extended support vector regression (X-SVR) (2019)Fatigue reliability analysis of wind turbine tower under random wind load (2020)Probabilistic Structural Dynamics: Advanced Theory and Applications (1967)On the numerical solution of the Fokker-Planck equation for nonlinear stochastic systems (1993)Numerical solution of stochastic differential equations (2016)Direct probability integral method for stochastic response analysis of static and dynamic structural systems (2019)Probabilistic Theory of Structural Dynamics (1976)Stochastic Differential Equations: An Introduction with Applications. (1987)Stochastic Differential Equations—An Introduction With Applications (2006)Random vibration analysis of structures by a time-domain explicit formulation method (2014)Comparison of PDEM and MCS: Accuracy and efficiency (2022)A decoupled approach for determination of the joint probability density function of a high-dimensional nonlinear stochastic dynamical system via the probability density evolution method (2023)Estimation of small failure probabilities in high dimensions by subset simulation (2001)Reliability analysis of structures with interval uncertainties under stationary stochastic excitations (2015)System reliability analyses of static and dynamic structures via direct probability integral method (2021)The stochastic finite-element method (1980)An analytical Wiener path integral technique for non-stationary response determination of nonlinear oscillators (2011)Stochastic Response Analysis of a Spar-Type FOWT Subjected to Extreme Waves by a Novel Filter Wave Model and the DR-PDEE (2024)Structural design optimization under stochastic excitations considering first-passage probability constraint based on dimension-reduced probability density evolution equation (2025)On the relation between ordinary and stochastic differential equations (1965)An exponential-spectral mapping method for solving probability density evolution equations of stochastic dynamical systems (2025)Stochastic Dynamics of Marine Structures (2012)Time-dependent reliability analysis with joint upcrossing rates (2013)Simulation of Ergodic Multivariate Stochastic Processes (1996)The stochastic finite element method: Past, present and future (2008)Fast Numerical Methods for Stochastic Computations: A Review (2009)A GF-discrepancy for point selection in stochastic seismic response analysis of structures with uncertain parameters (2015)Random function based spectral representation of stationary and non-stationary stochastic processes (2016)
this work references cited by second hop

References

  • 1991Simulation of Stochastic Processes by Spectral Representation1,379 cited
  • 2009Stochastic Dynamics of Structures923 cited
  • 2006The principle of preservation of probability and the generalized density evolution equation517 cited
  • 2011Random Vibrations: Analysis of Structural and Mechanical Systems473 cited
  • 2000Efficient path integration methods for nonlinear dynamic systems250 cited
  • 2011Advances of the probability density evolution method for nonlinear stochastic systems247 cited
  • 2008A note on the principle of preservation of probability and probability density evolution equation126 cited
  • 2013Reliability assessment in structural dynamics102 cited

Cited by

  • 2022Physically Driven Exact Dimension Reduction of a Class of Nonlinear Multidimensional Systems Subjected to Additive White Noise24 cited
  • 2025Efficient stochastic response analysis of high-dimensional nonlinear systems subject to multiplicative noise via the DR-PDEE20 cited
  • 2025DR-PDEE-based probabilistic response analysis for high-dimensional nonlinear dynamical systems under general non-white and non-stationary random excitations via constructing the auxiliary diffusion process15 cited
  • 2025Stochastic dynamic response analysis via dimension-reduced probability density evolution equation (DR-PDEE) with enhanced tail-accuracy14 cited
  • 2025Dimension-reduced Chapman-Kolmogorov equation for high-dimensional stochastic dynamical systems

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10 cited