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Monte Carlo and Quasi-Monte Carlo Methods 2008

:	Pierre L` Ecuyer, Art B. Owen
:	Pierre L' Ecuyer, Art B. Owen
:	Monte Carlo and Quasi-Monte Carlo Methods 2008
:	Springer-Verlag
:	9783642041075
:	1
:	CHF 134.60
:

:	Arithmetik, Algebra
:	English

:	672
:	Wasserzeichen
:	PC/MAC/eReader/Tablet
:	PDF

T is book represents the refereed proceedings of the Eighth International Conference on Monte Carlo (MC)and Quasi-Monte Carlo (QMC) Methods in Scientific Computing, held in Montreal (Canada) in July 2008. It covers the latest theoretical developments as well as important applications of these methods in different areas. It contains two tutorials, eight invited articles, and 32 carefully selected articles based on the 135 contributed presentations made at the conference. This conference is a major event in Monte Carlo methods and is the premiere event for quasi-Monte Carlo and its combination with Monte Carlo. This series of proceedings volumes is the primary outlet for quasi-Monte Carlo research.

	Preface	5
	Contents	8
	Part I Tutorials	12
	Monte Carlo and Quasi-Monte Carlo for Statistics	13
	Introduction	13
	The Bootstrap	14
	Permutation Tests	18
	MCMC	21
	Least Trimmed Squares	23
	Other Methods	26
	References	26
	Monte Carlo Computation in Finance	29
	Introduction	29
	Overview of Financial Simulation Problems	30
	Financial Simulations in Context	33
	Multiple Simulation Problems	35
	Variance Reduction	38
	Risk Management	42
	Financial Optimization Problems	43
	Sensitivity Analysis	44
	Discretization of Stochastic Differential Equations	46
	References	48
	Part II Invited Articles	53
	Particle Markov Chain Monte Carlo for Efficient Numerical Simulation	54
	Introduction	54
	Sequential Monte Carlo Methods	55
	Particle Independent MH Sampler	58
	Algorithm	59
	Extended Proposal and Target Distributions	59
	Structure of the Invariant Distribution and Alternative Algorithm	61
	Using All the Particles	62
	Particle Marginal MH Sampler and Particle Gibbs Sampler	62
	Particle Marginal MH Sampler	63
	Particle Gibbs Sampler	64
	Extensions and Discussion	65
	Application to Markov Jump Processes	66
	Conclusion	67
	References	69
	Computational Complexity of Metropolis-Hastings Methods in High Dimensions	70
	Introduction	70
	Structure of the Target	71
	Product Target	71
	Beyond the Product Structure	71
	Computational Complexity	73
	The Algorithms	74
	Complexity	75
	A Special Result: Diffusion Limit	76
	Open Questions	78
	References	80
	On Quasi-Monte Carlo Rules Achieving Higher Order Convergence	81
	Introduction	81
	Higher Order Convergence for Smooth Periodic Functions Using Lattice Rules	84
	Lattice Rules	84
	Decay of the Fourier Coefficients of Smooth Periodic Functions	84
	Numerical Integration	85
	Preliminaries	86
	The Digital Construction Scheme	86
	Walsh Functions	87
	Higher Order Convergence of Smooth Functions Using Generalized Digital Nets	88
	Decay of the Walsh Coefficients of Smooth Functions	88
	Numerical Integration	90
	Generalized Digital Nets	91
	Construction of Generalized Digital Nets	93
	Geometrical Properties of Generalized Digital Nets	95
	Geometrical Numerical Integration	98
	References	103
	Sensitivity Estimates for Compound Sums	105
	Introduction	105
	Motivating Applications	107
	Lévy Processes	107
	Stochastic Volatility and Squared Bessel Bridges	108
	Locally Continuous Construction	109
	Application to the Squared Bessel Bridge	116
	Globally Continuous Construction	118
	Concluding Remarks	120
	References	120
	New Perspectives on (0,s)-Sequences	121
	Introduction	121
	Background Information	122
	Framework of Generalized Niederreiter Sequences	126
	New Efficient Scramblings of (0,s)-Sequences	128
	A Construction Extensible in the Dimension--GF3	130
	Numerical Results	131
	Conclusion	135
	References	136
	Variable Subspace Sampling and Multi-level Algorithms	139
	Introduction	139
	Multi-level Algorithms	141
	A Cost Model for Variable Subspace Sampling	145
	Analysis of the Multi-level Algorithm	148
	General Results	148
	Lipschitz Continuous Integrands	151
	Minimal Errors in Different Cost Models	156
	Optimal Quadrature of Lipschitz Functionals	157
	Gaussian Measures	158
	Diffusion Processes	160
	Concluding Remarks	162
	References	163
	Markov Chain Monte Carlo Algorithms: Theory and Practice	165
	Introduction	165
	Asymptotic Convergence	166
	Quantitative Convergence Bounds	167
	Minorisation Conditions (Small Sets)	168
	Drift Conditions	168
	An Explicit Convergence Bound	169
	A 20-Dimensional Example	169
	Adaptive MCMC	171
	A Toy Example	171
	An Adaptive MCMC Convergence Theorem	172
	A 100-Dimensional Example	173
	Connection with QMC?	174
	Summary	175
	References	176
	MinT -- New Features and New Results	178
	Introduction	178
	Basic Notations and Concepts	179
	New Features in MinT	183
	New Nets based on OOA Propagation Rules	188
	A Generalized Matrix-Product Construction for Generalized Codes	191
	References	195
	Part III Contributed Articles	197
	Recursive Computation of Value-at-Risk and Conditional Value-at-Risk using MC and QMC	198
	Introduction	199
	Design of the VaR-CVaR Stochastic Approximation Algorithm	201
	Devise of a VaR-CVaR Procedure (First Phase)	201
	Variance Reduction Using Adaptive Recursive Importance Sampling (Final Phase)	204
	Quasi-Stochastic Approximation	210
	Numerical Illustrations	211
	References	213
	Adaptive Monte Carlo Algorithms Applied to Heterogeneous Transport Problems	214
	Introductio