Functional quantization of a class of Brownian diffusions : A constructive approach
Identifieur interne : 001575 ( Main/Exploration ); précédent : 001574; suivant : 001576Functional quantization of a class of Brownian diffusions : A constructive approach
Auteurs : Harald Luschgy [Allemagne] ; Gilles Pages [France]Source :
- Stochastic processes and their applications [ 0304-4149 ] ; 2006.
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- Pascal (Inist)
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Abstract
The functional quantization problem for one-dimensional Brownian diffusions on [0, T] is investigated. One shows under rather general assumptions that the rate of convergence of the Lp-quantization error is O((log n)-1/2) like for the Brownian motion. Several methods to construct some rate-optimal quantizers are proposed. These results are extended to d-dimensional diffusions when the diffusion coefficient is the inverse of a gradient function. Finally, a special attention is given to diffusions with a Gaussian martingale term.
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Jussieu</s1><s2>75252 Paris</s2><s3>FRA</s3><sZ>2 aut.</sZ></inist:fA14><country>France</country><placeName><region type="region" nuts="2">Île-de-France</region><settlement type="city">Paris</settlement></placeName></affiliation></author></analytic><series><title level="j" type="main">Stochastic processes and their applications</title><title level="j" type="abbreviated">Stochastic processes appl.</title><idno type="ISSN">0304-4149</idno><imprint><date when="2006">2006</date></imprint></series></biblStruct></sourceDesc><seriesStmt><title level="j" type="main">Stochastic processes and their applications</title><title level="j" type="abbreviated">Stochastic processes appl.</title><idno type="ISSN">0304-4149</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Brownian motion</term><term>Convergence rate</term><term>Diffusion coefficient</term><term>Diffusion process</term><term>Error estimation</term><term>Functional quantization</term><term>Lamperti transformation</term><term>Lp approximation</term><term>Martingale</term><term>Quantization</term><term>Stochastic process</term></keywords><keywords scheme="Pascal" xml:lang="fr"><term>Processus diffusion</term><term>Quantification</term><term>Taux convergence</term><term>Approximation Lp</term><term>Estimation erreur</term><term>Mouvement brownien</term><term>Coefficient diffusion</term><term>Martingale</term><term>Processus stochastique</term><term>Théorème Girsanov</term><term>Quantification fonctionnelle</term><term>Transformation Lamperti</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">The functional quantization problem for one-dimensional Brownian diffusions on [0, T] is investigated. One shows under rather general assumptions that the rate of convergence of the L<sup>p</sup>-quantization error is O((log n)<sup>-1/2</sup>) like for the Brownian motion. Several methods to construct some rate-optimal quantizers are proposed. These results are extended to d-dimensional diffusions when the diffusion coefficient is the inverse of a gradient function. Finally, a special attention is given to diffusions with a Gaussian martingale term.</div></front></TEI><affiliations><list><country><li>Allemagne</li><li>France</li></country><region><li>Île-de-France</li></region><settlement><li>Paris</li></settlement></list><tree><country name="Allemagne"><noRegion><name sortKey="Luschgy, Harald" sort="Luschgy, Harald" uniqKey="Luschgy H" first="Harald" last="Luschgy">Harald Luschgy</name></noRegion></country><country name="France"><region name="Île-de-France"><name sortKey="Pages, Gilles" sort="Pages, Gilles" uniqKey="Pages G" first="Gilles" last="Pages">Gilles Pages</name></region></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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