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Strategies for Quasi-Monte Carlo

Strategies for Quasi-Monte Carlo builds a framework to design and analyze strategies for randomized quasi-Monte Carlo (RQMC). One key to efficient simulation using RQMC is to structure problems to reveal a small set of important variables, their number being the effective dimension, while the other...

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Bibliographic Details
Main Author: Fox, Bennett L.
Format: eBook
Language:English
Published: New York, NY Springer US 1999, 1999
Edition:1st ed. 1999
Series:International Series in Operations Research & Management Science
Subjects:
Operations Research
Optimization
Programming Techniques
Computer Programming
Control Theory
Probability Theory
Systems Theory, Control
System Theory
Mathematical Optimization
Operations Research And Decision Theory
Probabilities
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 6.1 Brownian-bridge methods
  • 6.2 Overview of remaining sections
  • 6.3 Principal-components methods
  • 6.4 Piecewise approach
  • 6.5 Gaussian random fields
  • 6.6 A negative result
  • 6.7 Linear-algebra software
  • 7 Smoothing Summation
  • 7.1 Smoothing the naive estimator
  • 7.2 Smoothing importance sampling
  • 7.3 Multiple indices ? single index
  • 7.4 Properties
  • 7.5 Remarks
  • 8 Smoothing Variate Generation
  • 8.1 Applying it to one variate
  • 8.2 Applying it to several variates
  • 9 Analysis Of Variance
  • 9.1 Variance in the one-dimensional case
  • 9.2 Weakening the smoothness condition?
  • 9.3 Nested decomposition
  • 9.4 Dynamic blocks
  • 9.5 Stratification linked to quasi-Monte Carlo
  • 9.6 The second term
  • 10 Bernoulli Trials: Examples
  • 10.1 Linearity in trial indicators
  • 10.2 Continuous-state Markov chains
  • 10.3 Weight windows and skewness attenuation.-10.4 Network reliability
  • 11 Poisson Processes: Auxiliary Matter
  • 11.1 Generating ordered uniforms
  • 1 Introduction
  • 1.1 Setting up the (X, Y)-decomposition
  • 1.2 Examples
  • 1.3 Antecedents
  • 1.4 Exploiting the (X, Y)-decomposition
  • 1.5 A hybrid with RQMC
  • 1.6 Generating Gaussian processes: foretaste
  • 1.7 Scope of recursive conditioning
  • 1.8 Ranking variables
  • 2 Smoothing
  • 2.1 Poisson case
  • 2.2 Separable problems
  • 2.3 Brownian motion — finance — PDEs
  • 2.4 The Poisson case revisted
  • 2.5 General considerations
  • 3 Generating Poisson Processes
  • 3.1 Computational complexity
  • 3.2 Variance
  • 3.3 The median-based method
  • 3.4 The terminal pass
  • 3.5 The midpoint-based method
  • 3.6 Stochastic geometry
  • 3.7 Extensions
  • 4 Permuting Order Statistics
  • 4.1 Motivating example
  • 4.2 Approach
  • 4.3 Relation to Latin supercubes
  • 4.4 Comparison of anomalies blockwise
  • 5 GENERATING BERNOULLI TRIALS
  • 5.1 The third tree-like algorithm
  • 5.2 Variance
  • 5.3 Extensions
  • 5.4 q-Blocks
  • 6 Generating Gaussian Processes
  • 11.2 Generating betas
  • 11.3 Generating binomials
  • 11.4 Stratifying Poisson distributions
  • 11.5 Recursive variance quartering
  • 12 Background On Deterministic QMC
  • 12.1 The role of quasi-Monte Carlo
  • 12.2 Nets
  • 12.3 Discrepancy
  • 12.4 Truncating to get bounded variation
  • 12.5 Electronic access
  • 13 OPTIMIZATION
  • 13.1 Global optimization over the unit cube
  • 13.2 Dynamic programming over the unit cube
  • 13.3 Stochastic programming
  • 14 Background on Randomized QMC
  • 14.1 Randomizing nets
  • 14.2 Randomizing lattices
  • 14.3 Latin hypercubes
  • 14.4 Latin supercubes
  • 15 Pseudocodes
  • 15.1 Randomizing nets
  • 15.2 Poisson processes: via medians
  • 15.3 Poisson processes: via midpoints
  • 15.4 Bernoulli trials: via equipartitions
  • 15.5 Order statistics: positioning extremes
  • 15.6 Generating ordered uniforms
  • 15.7 Discrete summation: index recovery

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