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76,796
Fast convergence of quasi–Monte Carlo for a class of isotropic integrals
 Math. Comp
, 2001
"... Abstract. We consider the approximation of ddimensional weighted integrals of certain isotropic functions. We are mainly interested in cases where d is large. We show that the convergence rate of quasiMonte Carlo for the approximation of these integrals is O ( √ log n/n). Since this is a worst ca ..."
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Cited by 7 (0 self)
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Abstract. We consider the approximation of ddimensional weighted integrals of certain isotropic functions. We are mainly interested in cases where d is large. We show that the convergence rate of quasiMonte Carlo for the approximation of these integrals is O ( √ log n/n). Since this is a worst
QuasiMonte Carlo Integration
 JOURNAL OF COMPUTATIONAL PHYSICS
, 1995
"... The standard Monte Carlo approach to evaluating multidimensional integrals using (pseudo)random integration nodes is frequently used when quadrature methods are too difficult or expensive to implement. As an alternative to the random methods, it has been suggested that lower error and improved con ..."
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Cited by 72 (6 self)
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The standard Monte Carlo approach to evaluating multidimensional integrals using (pseudo)random integration nodes is frequently used when quadrature methods are too difficult or expensive to implement. As an alternative to the random methods, it has been suggested that lower error and improved
Sufficient conditions for fast quasiMonte Carlo convergence
 J. Complexity
, 2003
"... We study the approximation of ddimensional integrals. We present sufficient conditions for fast quasiMonte Carlo convergence. They apply to isotropic and nonisotropic problems and, in particular, to a number of problems in computational finance. We show that the convergence rate of quasiMonte Ca ..."
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Cited by 7 (0 self)
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We study the approximation of ddimensional integrals. We present sufficient conditions for fast quasiMonte Carlo convergence. They apply to isotropic and nonisotropic problems and, in particular, to a number of problems in computational finance. We show that the convergence rate of quasiMonte
When are QuasiMonte Carlo Algorithms Efficient for High Dimensional Integrals?
 J. Complexity
, 1997
"... Recently quasiMonte Carlo algorithms have been successfully used for multivariate integration of high dimension d, and were significantly more efficient than Monte Carlo algorithms. The existing theory of the worst case error bounds of quasiMonte Carlo algorithms does not explain this phenomenon. ..."
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Cited by 183 (23 self)
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. This paper presents a partial answer to why quasiMonte Carlo algorithms can work well for arbitrarily large d. It is done by identifying classes of functions for which the effect of the dimension d is negligible. These are weighted classes in which the behavior in the successive dimensions is moderated by a
QuasiMonte Carlo Radiosity
, 1996
"... The problem of global illumination in computer graphics is described by a second kind Fredholm integral equation. Due to the complexity of this equation, Monte Carlo methods provide an interesting tool for approximating solutions to this transport equation. For the case of the radiosity equation, w ..."
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Cited by 40 (2 self)
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The problem of global illumination in computer graphics is described by a second kind Fredholm integral equation. Due to the complexity of this equation, Monte Carlo methods provide an interesting tool for approximating solutions to this transport equation. For the case of the radiosity equation
Sequential data assimilation with a nonlinear quasigeostrophic model using Monte Carlo methods to forecast error statistics
 J. Geophys. Res
, 1994
"... . A new sequential data assimilation method is discussed. It is based on forecasting the error statistics using Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter. The ..."
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Cited by 782 (22 self)
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. A new sequential data assimilation method is discussed. It is based on forecasting the error statistics using Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter
Sequential quasiMonte Carlo
, 2014
"... We develop a new class of algorithms, SQMC (Sequential QuasiMonte Carlo), as a variant of SMC (Sequential Monte Carlo) based on lowdiscrepancy point sets. The complexity of SQMC is O(N logN), where N is the number of simulations at each iteration, and its error rate is smaller than the Monte Carlo ..."
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Cited by 3 (2 self)
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We develop a new class of algorithms, SQMC (Sequential QuasiMonte Carlo), as a variant of SMC (Sequential Monte Carlo) based on lowdiscrepancy point sets. The complexity of SQMC is O(N logN), where N is the number of simulations at each iteration, and its error rate is smaller than the Monte
Halftoning and QuasiMonte Carlo
"... In performing statistical studies in simulation science, it is often necessary to estimate the value of an integral of a function that is based on a simulation calculation. Because simulations tend to be costly in terms of computer time and resources, the ability to accurately estimate integrals wit ..."
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Cited by 1 (0 self)
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with a minimum number of function evaluations is a critical issue in evaluating simulation codes. The goal in QuasiMonte Carlo (QMC) is to improve the accuracy of integrals estimated by the Monte Carlo technique through a suitable specification of the sample point set. Indeed, the errors from N samples
QUASIMONTE CARLO METHODS IN FINANCE
"... We review the basic principles of QuasiMonte Carlo (QMC) methods, the randomizations that turn them into variancereduction techniques, and the main classes of constructions underlying their implementations: lattice rules, digital nets, and permutations in different bases. QMC methods are designed t ..."
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We review the basic principles of QuasiMonte Carlo (QMC) methods, the randomizations that turn them into variancereduction techniques, and the main classes of constructions underlying their implementations: lattice rules, digital nets, and permutations in different bases. QMC methods are designed
Results 1  10
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76,796