Monte Carlo and Quasi-Monte Carlo Methods (eBook)

Part I Invited papers.- Multilevel Monte Carlo Implementation for SDEs driven by Truncated Stable Processes.- Construction of a Mean Square Error Adaptive Euler–Maruyama Method With Applications in Multilevel Monte Carlo.- Vandermonde Nets and Vandermonde Sequences.- Path Space Markov Chain Monte Carlo Methods in Computer Graphics.- Walsh Figure of Merit for Digital Nets: An Easy Measure for Higher Order Convergent QMC.- Some Results on the Complexity of Numerical Integration.- Approximate Bayesian Computation: A Survey on Recent Results.- Part II Contributed papers.- Multilevel Monte Carlo Simulation of Statistical Solutions to the Navier–Stokes Equations.- Unbiased Simulation of Distributions with Explicitly Known Integral Transforms.- Central Limit Theorem for Adaptive Multilevel Splitting Estimators in an Idealized Setting.- Comparison between LS-Sequences and β -adic van der Corput Sequences.- Computational Higher Order Quasi-Monte Carlo Integration.- Numerical Computation of Multivariate Normal Probabilities using Bivariate Conditioning.- Non-nested Adaptive Timesteps in Multilevel Monte Carlo Computations.- On ANOVA Decompositions of Kernels and Gaussian Random Field Paths.- The Mean Square Quasi-Monte Carlo Error for Digitally Shifted Digital Nets.- Uncertainty and Robustness in Weather Derivative Models.- Reliable Adaptive Cubature Using Digital Sequences.- Optimal Point Sets for Quasi-Monte Carlo Integration of Bivariate Periodic Functions with Bounded Mixed Derivatives.- Adaptive Multidimensional Integration Based on Rank-1 Lattices.- Path Space Filtering.- Tractability of Multivariate Integration in Hybrid Function Spaces.- Derivative-based Global Sensitivity Measures and Their Link with Sobol’ Sensitivity Indices.- Bernstein Numbers and Lower Bounds for the Monte Carlo Error.- A Note on the Importance of Weak Convergence Rates for SPDE Approximations in Multilevel Monte Carlo Schemes.- A Strategy for Parallel Implementations of Stochastic Lagrangian Simulation.- A New Rejection Sampling Method for Truncated Multivariate Gaussian Random Variables Restricted to Convex Sets.- Van der Corput and Golden Ratio Sequences Along the Hilbert Space-Filling Curve.- Uniform Weak Tractability of Weighted Integration.- Incremental Greedy Algorithm and Its Applications in Numerical Integration.- On “Upper Error Bounds for Quadrature Formulas on Function Classes” by K K Frolov.- Tractability of Function Approximation With Product Kernels.- Discrepancy Estimates for Acceptance-Rejection Samplers Using Stratified Inputs.- List of Participants.- Index.