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QUANTIFYING UNCERTAIN SYSTEM OUTPUTS VIA THE MULTI-LEVEL MONTE CARLO METHOD-DISTRIBUTION AND ROBUSTNESS MEASURES
15 references·1 citing·38 second hop
QUANTIFYING UNCERTAIN SYSTEM OUTPUTS VIA THE MULTI-LEVEL MONTE CARLO METHOD-DISTRIBUTION AND ROBUSTNESS MEASURES (2023)QUANTIFYING UNCERTAIN SYSTEM OUTPUTS VIA …Quantifying uncertain system outputs via the multilevel Monte Carlo method — Part I: Central moment estimation (2020)Quantifying uncertain system …Estimation of distributions via multilevel Monte Carlo with stratified sampling (2020)Estimation of distributions v…Multilevel Nested Simulation for Efficient Risk Estimation (2019)Multilevel Nested Simulation …A Continuation Multi Level Monte Carlo (C-MLMC) method for uncertainty quantification in compressible inviscid aerodynamics (2017)A Continuation Multi Level Mo…Approximation of probability density functions by the Multilevel Monte Carlo Maximum Entropy method (2016)Approximation of probability …Multilevel Monte Carlo Approximation of Distribution Functions and Densities (2015)Multilevel Monte Carlo Approx…A continuation multilevel Monte Carlo algorithm (2014)A continuation multilevel Mon…Spectral Methods for Uncertainty Quantification (2010)Spectral Methods for Uncertai…On irregular functionals of SDEs and the Euler scheme (2009)On irregular functionals of S…Analysing multi-level Monte Carlo for options with non-globally Lipschitz payoff (2009)Analysing multi-level Monte C…Multilevel Monte Carlo Path Simulation (2008)Multilevel Monte Carlo Path S…A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2007)A Stochastic Collocation Meth…The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)The Wiener--Askey Polynomial …Conditional value-at-risk for general loss distributions (2002)Conditional value-at-risk for…Conditional Value-at-Risk: Optimization Approach (2001)Conditional Value-at-Risk: Op…An Approximate Control Variates Approach to Multifidelity Distribution Estimation (2024)An Approximate Control Variat…High-Order Collocation Methods for Differential Equations with Random Inputs (2005)A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2008)An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis (2009)Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization (2018)Asymptotic error distributions for the Euler method for stochastic differential equations (1998)Stochastic Calculus for Finance II: Continuous-Time Models (2004)An improved multilevel Monte Carlo method for estimating probability distribution functions in stochastic oil reservoir simulations (2016)Iterative multilevel particle approximation for McKean–Vlasov SDEs (2019)Brownian Motion and Stochastic Calculus (2007)Stopped diffusion processes: Boundary corrections and overshoot (2009)Numerical solution of stochastic differential equations (2016)Stochastic Finite Elements: A Spectral Approach (1991)Global sensitivity analysis using polynomial chaos expansions (2007)Adaptive sparse polynomial chaos expansion based on least angle regression (2010)Monte Carlo Methods in Financial Engineering (2003)Stochastic differential equations and applications (2008)Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equations (2013)An Explicit Euler Scheme with Strong Rate of Convergence for Financial SDEs with Non-Lipschitz Coefficients (2016)Stochastic Differential Equations (1998)A Multilevel Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2015)Unbiased Estimation with Square Root Convergence for SDE Models (2015)Fast Bayesian experimental design: Laplace-based importance sampling for the expected information gain (2018)A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options (1993)Multi-level Monte Carlo Finite Element method for elliptic PDEs with stochastic coefficients (2011)Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients (2012)Optimal Model Management for Multifidelity Monte Carlo Estimation (2016)PORTFOLIO SELECTION* (1952)Coherent Measures of Risk (1999)Optimization of conditional value-at-risk (2000)Optimization with Stochastic Dominance Constraints (2003)Stochastic Programming Models (2003)Robust Optimization for Unconstrained Simulation-Based Problems (2009)Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients (2011)Simulation-based optimal Bayesian experimental design for nonlinear systems (2012)An Introduction to Computational Stochastic PDEs (2014)On the coherence of expected shortfall (2002)Spectral measures of risk: A coherent representation of subjective risk aversion (2002)Making and Evaluating Point Forecasts (2011)
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References

  • 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 cited
  • 2002Conditional value-at-risk for general loss distributions3,847 cited
  • 2008Multilevel Monte Carlo Path Simulation1,445 cited
  • 2007A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data1,396 cited
  • 2010Spectral Methods for Uncertainty Quantification953 cited
  • 2001Conditional Value-at-Risk: Optimization Approach153 cited
  • 2014A continuation multilevel Monte Carlo algorithm121 cited
  • 2009On irregular functionals of SDEs and the Euler scheme85 cited
  • 2009Analysing multi-level Monte Carlo for options with non-globally Lipschitz payoff78 cited
  • 2015Multilevel Monte Carlo Approximation of Distribution Functions and Densities70 cited
  • 2016Approximation of probability density functions by the Multilevel Monte Carlo Maximum Entropy method52 cited
  • 2017A Continuation Multi Level Monte Carlo (C-MLMC) method for uncertainty quantification in compressible inviscid aerodynamics51 cited
  • 2020Quantifying uncertain system outputs via the multilevel Monte Carlo method — Part I: Central moment estimation38 cited
  • 2019Multilevel Nested Simulation for Efficient Risk Estimation38 cited

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2020
Estimation of distributions via multilevel Monte Carlo with stratified sampling
30 cited

Cited by

  • 2024An Approximate Control Variates Approach to Multifidelity Distribution Estimation6 cited