Fast orthogonal transforms and generation of Brownian paths

Gunther Leobacher

doi:10.1016/j.jco.2011.11.003

Fast orthogonal transforms and generation of Brownian paths

Gunther Leobacher

Institute of Financial Mathematics and Applied Number Theory

Research output: Contribution to journal › Article › peer-review

Abstract

We present a number of fast constructions of discrete Brownian paths that can be used as alternatives to principal component analysis and Brownian bridge for stratified Monte Carlo and quasi-Monte Carlo. By fast we mean that a path of length $n$ can be generated in $O(n\log(n))$ floating point operations. We highlight some of the connections between the different constructions and we provide some numerical examples.

Original language	English
Pages (from-to)	278-302
Number of pages	25
Journal	Journal of Complexity
Volume	28
Issue number	2
DOIs	https://doi.org/10.1016/j.jco.2011.11.003
Publication status	Published - Apr 2012

Fields of science

101025 Number theory
101 Mathematics

JKU Focus areas

Computation in Informatics and Mathematics

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10.1016/j.jco.2011.11.003

Cite this

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abstract = "We present a number of fast constructions of discrete Brownian paths that can be used as alternatives to principal component analysis and Brownian bridge for stratified Monte Carlo and quasi-Monte Carlo. By fast we mean that a path of length \$n\$ can be generated in \$O(n\textbackslash{}log(n))\$ floating point operations. We highlight some of the connections between the different constructions and we provide some numerical examples.",

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AB - We present a number of fast constructions of discrete Brownian paths that can be used as alternatives to principal component analysis and Brownian bridge for stratified Monte Carlo and quasi-Monte Carlo. By fast we mean that a path of length $n$ can be generated in $O(n\log(n))$ floating point operations. We highlight some of the connections between the different constructions and we provide some numerical examples.

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DO - 10.1016/j.jco.2011.11.003

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Fast orthogonal transforms and generation of Brownian paths

Abstract

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Quasi-Monte Carlo for Portfolio-Credit-Derivates

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Fast orthogonal transforms and generation of Brownian paths

Abstract

Fields of science

JKU Focus areas

Access to Document

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Quasi-Monte Carlo for Portfolio-Credit-Derivates

Cite this