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Path integral solution for nonlinear systems under parametric Poissonian white noise input
3 references·16 citing·37 second hop
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(1976)Fast cell-to-cell mapping (path integration) for nonlinear white noise and Poisson driven systems (1995)Solution techniques for pulse problems in non-linear stochastic dynamics (2000)Stochastic Differential Equations (2006)Random vibration and statistical linearization (1990)Stochastic Dynamics of Structures (2009)A Wiener Path Integral Formalism for Treating Nonlinear Systems with Non-Markovian Response Processes (2022)A Wiener path integral technique for determining the stochastic response of nonlinear oscillators with fractional derivative elements: A constrained variational formulation with free boundaries (2023)Method for Random Vibration of Hysteretic Systems (1976)Estimation of small failure probabilities in high dimensions by subset simulation (2001)First-passage probability estimation of high-dimensional nonlinear stochastic dynamic systems by a fractional moments-based mixture distribution approach (2022)Reliability analysis of discrete-state performance functions via adaptive sequential sampling with detection of failure surfaces (2022)Probabilistic Structural Dynamics: Advanced Theory and Applications (1967)Applied Stochastic Processes and Control for Jump-Diffusions: Modeling, Analysis and Computation (2007)An analytical Wiener path integral technique for non-stationary response determination of nonlinear oscillators (2011)A new path integration method for the stochastic system under Poisson white noise excitation based on a probability mapping (2023)Probabilistic response determination of high-dimensional nonlinear dynamical systems enforced by parametric multiple Poisson white noises (2024)Equivalent linearization for Poisson white noise input (1995)Monte Carlo simulation in the stochastic analysis of non-linear systems under external stationary Poisson white noise input (2003)Transient response of Bouc–Wen hysteretic system under random excitation via RBFNN method (2022)Equivalent linearization and Monte Carlo simulation in stochastic dynamics (2003)Stochastic response determination of nonlinear oscillators with fractional derivatives elements via the Wiener path integral (2014)Stochastic averaging: An approximate method of solving random vibration problems (1986)Simulation and the Monte Carlo Method (2007)A sampling-variability-free dimension-reduced probability density evolution equation method for high-dimensional nonlinear stochastic dynamic analysis (2025)Efficient stochastic response analysis of high-dimensional nonlinear systems subject to multiplicative noise via the DR-PDEE (2025)The principle of preservation of probability and the generalized density evolution equation (2006)AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation (2011)
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References

  • 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 method83 cited
  • 1995Response and Reliability of Poisson-Driven Systems by Path Integration63 cited

Cited by

  • 2020An approach to evaluation of EVD and small failure probabilities of uncertain nonlinear structures under stochastic seismic excitations44 cited
  • 2022Reliability of dynamical systems with combined Gaussian and Poisson white noise via path integral method35 cited
  • 2025First excursion probability of dynamical systems: A review on computational methods32 cited
  • 2022Response of nonlinear oscillators with fractional derivative elements under evolutionary stochastic excitations: A Path Integral approach based on Laplace’s method of integration32 cited
  • 2020Path Integral Methods for the Probabilistic Analysis of Nonlinear Systems Under a White-Noise Process30 cited
  • 2022RBFNN for Calculating the Stationary Response of SDOF Nonlinear Systems Excited by Poisson White Noise23 cited
  • 2024Efficient path integral approach via analytical asymptotic expansion for nonlinear systems under Gaussian white noise22 cited
  • 2019A novel method based on augmented Markov vector process for the time-variant extreme value distribution of stochastic dynamical systems enforced by Poisson white noise21 cited
  • 2019Path Integral approach via Laplace’s method of integration for nonstationary response of nonlinear systems

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20 cited
  • 2022Stochastic dynamic analysis of nonlinear MDOF systems under combined Gaussian and Poisson noise excitation based on DPIM19 cited
  • 2020An improved path integration method for nonlinear systems under Poisson white noise excitation18 cited
  • 2022Response Statistics of Single-Degree-of-Freedom Systems with Lévy Noise by Improved Path Integral Method14 cited
  • 2023Response and reliability of suspension system under stochastic and periodic track excitations by path integral method13 cited
  • 2022A path integration algorithm for stochastic dynamical systems with multiple non-smooth events13 cited
  • 2025Dimension-reduced Chapman-Kolmogorov equation for high-dimensional stochastic dynamical systems10 cited
  • 2024Probabilistic analysis of nonlinear oscillators under correlated multi-power velocity multiplicative excitation and additive excitation7 cited