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Uncertainty quantification for stochastic nonlinear systems using Perron-Frobenius operator and Karhunen-Loève expansion
9 references·0 citing·29 second hop
Uncertainty quantification for stochastic nonlinear systems using Perron-Frobenius operator and Karhunen-Loève expansion (2012)Uncertainty quantification for stochastic…Dispersion Analysis in Hypersonic Flight During Planetary Entry Using Stochastic Liouville Equation (2011)Dispersion Analysis in Hypers…Beyond Monte Carlo: A Computational Framework for Uncertainty Propagation in Planetary Entry, Descent and Landing (2010)Beyond Monte Carlo: A Computa…High-Order Collocation Methods for Differential Equations with Random Inputs (2005)High-Order Collocation Method…Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure (2004)Physical Systems with Random …Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes (2004)Numerical Challenges in the U…Statistics for Spatial Data (1993)Statistics for Spatial DataStochastic Finite Elements: A Spectral Approach (1991)Stochastic Finite Elements: A…Brownian motion and stochastic calculus (1991)Brownian motion and stochasti…Stochastic Finite Element Expansion for Random Media (1989)Stochastic Finite Element Exp…Neumann Expansion for Stochastic Finite Element Analysis (1988)Polynomial Chaos in Stochastic Finite Elements (1990)A nonparametric model of random uncertainties for reduced matrix models in structural dynamics (2000)A generalized dimension‐reduction method for multidimensional integration in stochastic mechanics (2004)The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)Stochastic spectral methods for efficient Bayesian solution of inverse problems (2006)The Malliavin Calculus and Related Topics (2006)Simulation-based optimal Bayesian experimental design for nonlinear systems (2012)Propagation of Initial Mass Uncertainty in Aircraft Cruise Flight (2013)Tractable Expressions for Nonlinearly Propagated Uncertainties (2015)High-dimensional uncertainty quantification for Mars atmospheric entry using adaptive generalized polynomial chaos (2020)Applied Mathematical Sciences (2021)Large Sample Properties of Simulations Using Latin Hypercube Sampling (1987)A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2007)A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2008)Adaptive sparse polynomial chaos expansion based on least angle regression (2010)Global sensitivity analysis using polynomial chaos expansions (2007)AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation (2011)The asymptotic elasticity of utility functions and optimal investment in incomplete markets (1999)Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-form Approximation Approach (2002)A Tale of Two Time Scales: Determining Integrated Volatility with Noisy High Frequency Data (2003)Fast Numerical Methods for Stochastic Computations: A Review (2009)On the convergence of generalized polynomial chaos expansions (2011)Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion (2012)A novel stochastic collocation method for uncertainty propagation in complex mechanical systems (2014)Closed-Loop Adaptive Monte Carlo Framework for Uncertainty Forecasting in Nonlinear Dynamic Systems (2019)Multivariable geostatistics in S: the gstat package (2004)Methods to account for spatial autocorrelation in the analysis of species distributional data: a review (2007)An Explicit Link between Gaussian Fields and Gaussian Markov Random Fields: The Stochastic Partial Differential Equation Approach (2011)
this work references cited by second hop

References

  • 1993Statistics for Spatial Data6,517 cited
  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 1991Brownian motion and stochastic calculus2,089 cited
  • 2005High-Order Collocation Methods for Differential Equations with Random Inputs1,522 cited
  • 2004Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure609 cited
  • 1989Stochastic Finite Element Expansion for Random Media512 cited
  • 2004Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes451 cited
  • 2011Dispersion Analysis in Hypersonic Flight During Planetary Entry Using Stochastic Liouville Equation98 cited
  • 2010Beyond Monte Carlo: A Computational Framework for Uncertainty Propagation in Planetary Entry, Descent and Landing20 cited

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