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Random cubatures and quasi-Monte Carlo methods
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Veröffentlicht/Copyright:
5. Mai 2015
Abstract
We establish and examine the deep connection between highly stratified random cubature formulas and quasi-Monte Carlo methods. A class of such formulas, designed to exactly integrate the introduced generalized s-dimensional Haar system, is shown to have additional variance reduction compared to the known theoretical upper bound. We propose several equivalent expressions for the variance within the standard quasi-Monte Carlo setting. The theory of random cubatures is supplemented with both refined versions of known results and completely new facts.
Keywords: Monte Carlo; quasi-Monte Carlo; high-dimensional integration; stratified sampling; random cubature formulas; Sobol sequences
Funding source: RFBR
Award Identifier / Grant number: 14-01-00271
Received: 2015-2-24
Accepted: 2015-4-24
Published Online: 2015-5-5
Published in Print: 2015-9-1
© 2015 by De Gruyter
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Artikel in diesem Heft
- Frontmatter
- Random cubatures and quasi-Monte Carlo methods
- Numerical solution of an inverse problem of coefficient recovering for a wave equation by a stochastic projection methods
- Simulating from the Heston model: A gamma approximation scheme
- Reliability and accuracy in the space Lp(T) for the calculation of integrals depending on a parameter by the Monte Carlo method
- A new numerical scheme for the CIR process
Schlagwörter für diesen Artikel
Monte Carlo;
quasi-Monte Carlo;
high-dimensional integration;
stratified sampling;
random cubature formulas;
Sobol sequences
Artikel in diesem Heft
- Frontmatter
- Random cubatures and quasi-Monte Carlo methods
- Numerical solution of an inverse problem of coefficient recovering for a wave equation by a stochastic projection methods
- Simulating from the Heston model: A gamma approximation scheme
- Reliability and accuracy in the space Lp(T) for the calculation of integrals depending on a parameter by the Monte Carlo method
- A new numerical scheme for the CIR process
