## Monte Carlo and Quasi-Monte Carlo Methods: MCQMC, Leuven, Belgium, April 2014This book presents the refereed proceedings of the Eleventh International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at the University of Leuven (Belgium) in April 2014. These biennial conferences are major events for Monte Carlo and quasi-Monte Carlo researchers. The proceedings include articles based on invited lectures as well as carefully selected contributed papers on all theoretical aspects and applications of Monte Carlo and quasi-Monte Carlo methods. Offering information on the latest developments in these very active areas, this book is an excellent reference resource for theoreticians and practitioners interested in solving high-dimensional computational problems, arising, in particular, in finance, statistics and computer graphics. |

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### Contents

2 | |

3 | |

28 | |

Vandermonde Nets and Vandermonde Sequences | 87 |

Path Space Markov Chain Monte Carlo Methods in Computer Graphics | 107 |

An Easy Measure for Higher Order Convergent QMC | 142 |

Some Results on the Complexity of Numerical Integration | 161 |

A Survey on Recent Results | 185 |

Reliable Adaptive Cubature Using Digital Sequences | 367 |

Optimal Point Sets for QuasiMonte Carlo Integration of Bivariate Periodic Functions with Bounded Mixed Derivatives | 384 |

Adaptive Multidimensional Integration Based on Rank1 Lattices | 407 |

Path Space Filtering | 423 |

Tractability of Multivariate Integration in Hybrid Function Spaces | 437 |

DerivativeBased Global Sensitivity Measures and Their Link with Sobol Sensitivity Indices | 455 |

Bernstein Numbers and Lower Bounds for the Monte Carlo Error | 470 |

A Note on the Importance of Weak Convergence Rates for SPDE Approximations in Multilevel Monte Carlo Schemes | 489 |

Part II Contributed Papers | 206 |

Multilevel Monte Carlo Simulation of Statistical Solutions to the NavierStokes Equations | 209 |

Unbiased Simulation of Distributions with Explicitly Known Integral Transforms | 228 |

Central Limit Theorem for Adaptive Multilevel Splitting Estimators in an Idealized Setting | 245 |

Comparison Between LSSequences and βAdic van der Corput Sequences | 261 |

Computational Higher Order QuasiMonte Carlo Integration | 271 |

Numerical Computation of Multivariate Normal Probabilities Using Bivariate Conditioning | 289 |

Nonnested Adaptive Timesteps in Multilevel Monte Carlo Computations | 303 |

On ANOVA Decompositions of Kernels and Gaussian Random Field Paths | 315 |

The Mean Square QuasiMonte Carlo Error for Digitally Shifted Digital Nets | 331 |

Uncertainty and Robustness in Weather Derivative Models | 351 |

A Strategy for Parallel Implementations of Stochastic Lagrangian Simulation | 507 |

A New Rejection Sampling Method for Truncated Multivariate Gaussian Random Variables Restricted to Convex Sets | 521 |

Van der Corput and Golden Ratio Sequences Along the Hilbert SpaceFilling Curve | 531 |

Uniform Weak Tractability of Weighted Integration | 545 |

Incremental Greedy Algorithm and Its Applications in Numerical Integration | 556 |

On Upper Error Bounds for Quadrature Formulas on Function Classes by KK Frolov | 571 |

Tractability of Function Approximation with Product Kernels | 583 |

Discrepancy Estimates For AcceptanceRejection Samplers Using Stratified Inputs | 599 |

620 | |

### Other editions - View all

Monte Carlo and Quasi-Monte Carlo Methods: MCQMC, Leuven, Belgium, April 2014 Ronald Cools,Dirk Nuyens No preview available - 2016 |

### Common terms and phrases

adaptive algorithm Approximate Bayesian computation approximation Bayesian Carlo and Quasi-Monte Complex Comput condition consider construction convergence rate convex Corput sequence cubature defined denote density derivatives digital nets dimension discrepancy distribution error bound estimator example finite Fourier function Gaussian given golden ratio Hilbert spaces inequality input integrand integration lattice rules Lemma Lévy Lévy process light paths light transport linear lower bound Math mesh MLMC algorithm Monte Carlo methods MSE adaptive multilevel Monte Carlo multivariate Niederreiter number of samples Nuyens obtain optimal parameters path space photon mapping point sets polynomial tractability problem proof Quasi-Monte Carlo Methods random numbers random variable rejection sampling Sect simulation Sobol Sobolev spaces solution space-filling curve specular stochastic Theorem timestep truncated University upper bound values variance vector WAFOM Walsh coefficients weights